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**163**.

## Article

Hu, Liangjian and Li, Xiaoyue and Mao, Xuerong
(2018)
*Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations.*
Journal of Computational and Applied Mathematics, 337.
pp. 274-289.
ISSN 0377-0427

Song, Minghui and Mao, Xuerong
(2018)
*Almost sure exponential stability of hybrid stochastic functional differential equations.*
Journal of Mathematical Analysis and Applications, 458 (2).
pp. 1390-1408.
ISSN 0022-247X

Li, Xiaoyue and Mao, Xuerong and Yin, George
(2018)
*Explicit numerical approximations for stochastic differential equations in finite and infinite horizons : truncation methods, convergence in pth moment, and stability.*
IMA Journal of Numerical Analysis.
pp. 1-36.
ISSN 0272-4979
(In Press)

Guo, Qian and Liu, Wei and Mao, Xuerong and Yue, Rong-xian
(2018)
*The truncated Milstein method for stochastic differential equations with commutative noise.*
Journal of Computational and Applied Mathematics.
ISSN 0377-0427
(In Press)

Mo, Haoyi and Li, Mengling and Deng, Feiqi and Mao, Xuerong
(2017)
*Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps.*
Science in China Series F - Information Sciences.
ISSN 1009-2757
(In Press)

Song, Gongfei and Mao, Xuerong and Li, Tao
(2017)
*Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations.*
International Journal of Control.
pp. 1-17.
ISSN 0020-7179
(In Press)

Wu, Xiaotai and Tang, Yang and Cao, Jinde and Mao, Xuerong
(2017)
*Stability analysis for continuous-time switched systems with stochastic switching signals.*
IEEE Transactions on Automatic Control.
ISSN 0018-9286

Mao, Wei and Hu, Liangjian and You, Surong and Mao, Xuerong
(2017)
*Successive approximation of solutions to doubly perturbed stochastic differential equations with jumps.*
Electronic Journal of Qualitative Theory of Differential Equations, 86.
pp. 1-19.

Li, Mengling and Deng, Feiqi and Mao, Xuerong
(2017)
*Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps.*
Science in China Series F - Information Sciences.
ISSN 1009-2757
(In Press)

Song, Gongfei and Lu, Zhenyu and Zheng, Bo-chao and Mao, Xuerong
(2017)
*Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state.*
Science in China Series F - Information Sciences.
ISSN 1009-2757
(In Press)

Guo, Qian and Mao, Xuerong and Yue, Rongxian
(2017)
*The truncated Euler-Maruyama method for stochastic differential delay equations.*
Numerical Algorithms.
ISSN 1017-1398

Dong, Ran and Mao, Xuerong
(2017)
*On pth moment stabilization of hybrid systems by discrete-time feedback control.*
Stochastic Analysis and Applications.
ISSN 0736-2994

Fei, Weiyin and Hu, Liangjian and Mao, Xuerong and Shen, Mingxuan
(2017)
*Delay dependent stability of highly nonlinear hybrid stochastic systems.*
Automatica, 82.
pp. 165-170.
ISSN 0005-1098

Guo, Qian and Liu, Wei and Mao, Xuerong and Zhan, Weijun
(2017)
*Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations.*
International Journal of Computer Mathematics.
ISSN 0020-7160

Mao, Wei and Hu, Liangjian and Mao, Xuerong
(2017)
*Neutral stochastic functional differential equations with Levy jumps under the local Lipschitz condition.*
Advances in Difference Equations, 57.
pp. 1-24.
ISSN 1687-1847

Lu, Jianqiu and Li, Yuyuan and Mao, Xuerong and Qiu, Qinwei
(2017)
*Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations.*
Asian Journal of Control.
pp. 1-10.
ISSN 1561-8625
(In Press)

Guo, Qian and Liu, Wei and Mao, Xuerong and Yue, Rongxian
(2017)
*The partially truncated Euler-Maruyama method and its stability and boundedness.*
Applied Numerical Mathematics.
ISSN 0168-9274
(In Press)

Su, Huan and Mao, Xuerong and Li, Wenxue
(2016)
*Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller.*
Chaos: An Interdisciplinary Journal of Nonlinear Science, 26 (11).
pp. 1-20.
ISSN 1054-1500

Greenhalgh, D. and Liang, Y. and Mao, X.
(2016)
*Modelling the effect of telegraph noise in the SIRS epidemic model using Markovian switching.*
Physica A: Statistical Mechanics and its Applications, 462.
pp. 684-704.
ISSN 0378-4371

Song, Gongfei and Zheng, Bo-Chao and Luo, Qi and Mao, Xuerong
(2016)
*Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode.*
Control Theory and Applications.
ISSN 1751-8644

Li, Yuyuan and Lu, Jianqiu and Kou, Chunhai and Mao, Xuerong and Pan, Jiafeng
(2016)
*Robust stabilization of hybrid uncertain stochastic systems by discrete-time feedback control.*
Optimal Control Applications and Methods.
pp. 1-20.
ISSN 0143-2087
(In Press)

Zhao, Yanan and Lin, Yuguo and Jiang, Daqing and Mao, Xuerong and Li, Yong
(2016)
*Stationary distribution of stochastic SIRS epidemic model with standard incidence.*
Discrete and Continuous Dynamical Systems - Series B, 21 (7).
pp. 2363-2378.
ISSN 1531-3492

Feng, Lichao and Li, Shoumei and Mao, Xuerong
(2016)
*Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching.*
Journal of the Franklin Institute.
ISSN 0016-0032
(In Press)

Qiu, Qinwei and Liu, Wei and Hu, Liangjian and Mao, Xuerong and You, Surong
(2016)
*Stabilisation of stochastic differential equations with Markovian switching by feedback control based on discrete-time state observation with a time delay.*
Statistics and Probability Letters, 115.
pp. 16-26.
ISSN 0167-7152

Mao, Wei and You, Surong and Mao, Xuerong
(2016)
*On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps.*
Journal of Computational and Applied Mathematics.
ISSN 0377-0427

Guo, Qian and Mao, Xuerong and Yue, Rongxian
(2016)
*Almost sure exponential stability of stochastic differential delay equations.*
SIAM Journal on Control and Optimization, 54 (4).
pp. 1919-1933.
ISSN 0363-0129

Liu, Wei and Mao, Xuerong
(2016)
*Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations.*
Numerical Algorithms.
pp. 1-20.
ISSN 1017-1398

Mao, Xuerong
(2016)
*Almost sure exponential stabilization by discrete-time stochastic feedback control.*
IEEE Transactions on Automatic Control, 61 (6).
pp. 1619-1624.
ISSN 0018-9286

Mao, Xuerong
(2016)
*Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations.*
Journal of Computational and Applied Mathematics, 296.
pp. 362-375.
ISSN 0377-0427

Mao, Wei and Mao, Xuerong
(2016)
*An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure.*
Advances in Difference Equations, 2016 (1).
ISSN 1687-1847

Liang, Yanfeng and Greenhalgh, David and Mao, Xuerong
(2016)
*A stochastic differential equation model for the spread of HIV amongst people who inject drugs.*
Computational and Mathematical Methods in Medicine, 2016.
ISSN 1748-6718

Greenhalgh, D. and Liang, Y. and Mao, X.
(2016)
*SDE SIS epidemic model with demographic stochasticity and varying population size.*
Applied Mathematics and Computation, 276.
pp. 218-238.
ISSN 0096-3003

Mao, Xuerong
(2015)
*The truncated Euler–Maruyama method for stochastic differential equations.*
Journal of Computational and Applied Mathematics, 290.
370–384.
ISSN 0377-0427

Mao, Wei and Hu, Liangjian and Mao, Xuerong
(2015)
*The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps.*
Applied Mathematics and Computation, 268.
pp. 883-896.
ISSN 0096-3003

Greenhalgh, David and Liang, Yanfeng and Mao, Xuerong
(2015)
*Demographic stochasticity in the SDE SIS epidemic model.*
Discrete and Continuous Dynamical Systems - Series B, 20 (9).
pp. 2859-2884.
ISSN 1531-3492

Zhang, Liguo and Mao, Xuerong
(2015)
*Vehicle density estimation of freeway traffic with unknown boundary demand-supply : an IMM approach.*
IET Control Theory and Applications, 9 (13).
pp. 1989-1995.
ISSN 1751-8644

Feng, Ling and Huang, Zhigang and Mao, Xuerong
(2015)
*Mean percentage of returns for stock market linked savings accounts.*
Applied Mathematics and Computation.
ISSN 0096-3003
(In Press)

You, Surong and Mao, Wei and Mao, Xuerong and Hu, Liangjian
(2015)
*Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients.*
Applied Mathematics and Computation, 263.
73–83.
ISSN 0096-3003

You, Surong and Hu, Liangjian and Mao, Wei and Mao, Xuerong
(2015)
*Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations.*
Statistics and Probability Letters, 102.
pp. 8-16.

Liu, Wei and Mao, Xuerong
(2015)
*Numerical stationary distribution and its convergence for nonlinear stochastic differential equations.*
Journal of Computational and Applied Mathematics, 276.
pp. 16-29.
ISSN 0377-0427

Mao, Wei and You, Surong and Wu, Xiaoqian and Mao, Xuerong
(2015)
*On the averaging principle for stochastic delay differential equations with jumps.*
Advances in Difference Equations, 2015.
ISSN 1687-1847

Zhao, Yanan and Jiang, Daqing and Mao, Xuerong and Gray, Alison
(2015)
*The threshold of a stochastic SIRS epidemic model in a population with varying size.*
Discrete and Continuous Dynamical Systems - Series B, 20 (4).
pp. 1277-1295.
ISSN 1531-3492

Mao, Xuerong
(2015)
*Almost sure exponential stability in the numerical simulation of stochastic differential equations.*
SIAM Journal on Numerical Analysis, 53 (1).
pp. 370-389.
ISSN 0036-1429

You, Surong and Liu, Wei and Lu, Jianqiu and Mao, Xuerong and Qiu, Qinwei
(2015)
*Stabilization of hybrid systems by feedback control based on discrete-time state observations.*
SIAM Journal on Control and Optimization.
(In Press)

Mao, Wei and Zhu, Quanxin and Mao, Xuerong
(2014)
*Existence, uniqueness and almost surely asymptotic estimations of the solutions to neutral stochastic functional differential equations driven by pure jumps.*
Applied Mathematics and Computation.
ISSN 0096-3003
(In Press)

Mao, Xuerong and Liu, Wei and Hu, Liangjian and Luo, Qi and Lu, Jianqiu
(2014)
*Stabilization of hybrid stochastic differential equations by feedback control based on discrete-time state observations.*
Systems and Control Letters, 73.
pp. 88-95.
ISSN 0167-6911

Liu, Wei and Foondun, Mohammud and Mao, Xuerong
(2014)
*Mean square polynomial stability of numerical solutions to a class of stochastic differential equations.*
Statistics and Probability Letters, 92.
pp. 173-182.
ISSN 0167-7152

Pan, Jiafeng and Gray, Alison and Greenhalgh, David and Mao, Xuerong
(2014)
*Parameter estimation for the stochastic SIS epidemic model.*
Statistical Inference for Stochastic Processes, 17 (1).
pp. 75-98.
ISSN 1387-0874

Mao, Wei and Mao, Xuerong
(2014)
*On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions.*
Applied Mathematics and Computation, 230.
pp. 104-119.
ISSN 0096-3003

Yang, Qingshan and Mao, Xuerong
(2014)
*Stochastic dynamical behavior of SIRS epidemic models with random perturbation.*
Mathematical Biosciences and Engineering, 11 (4).
pp. 1003-1025.
ISSN 1547-1063

Xiong, Junlin and Lam, James and Shu, Zhan and Mao, Xuerong
(2014)
*Stability analysis of continuous-time switched systems with a random switching signal.*
IEEE Transactions on Automatic Control, 59 (1).
pp. 180-186.
ISSN 0018-9286

Mao, Xuerong and Song, Qingshuo and Yang, Dichuan
(2014)
*A note on exponential almost sure stability of stochastic differential equation.*
Bulletin of the Korean Mathematical Society, 51 (1).
pp. 221-227.
ISSN 2234-3016

Mao, Xuerong
(2013)
*Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control.*
Automatica, 49 (12).
pp. 3677-3681.
ISSN 0005-1098

Liu, Wei and Mao, Xuerong
(2013)
*Asymptotic moment boundedness of the numerical solutions of stochastic differential equations.*
Journal of Computational and Applied Mathematics, 251.
pp. 22-32.
ISSN 0377-0427

Liu, Wei and Mao, Xuerong
(2013)
*Strong convergence of the stopped Euler–Maruyama method for nonlinear stochastic differential equations.*
Applied Mathematics and Computation, 223.
pp. 389-400.
ISSN 0096-3003

Hu, Liangjian and Mao, Xuerong and Zhang, Liguo
(2013)
*Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations.*
IEEE Transactions on Automatic Control, 58 (9).
p. 2319.
ISSN 0018-9286

Song, Minghui and Hu, Liangjian and Mao, Xuerong and Zhang, Liguo
(2013)
*Khasminskii-type theorems for stochastic functional differential equations.*
Discrete and Continuous Dynamical Systems - Series B, 18 (6).
pp. 1697-1714.
ISSN 1531-3492

Yang, Qingshan and Mao, Xuerong
(2013)
*Extinction and recurrence of multi-group SEIR epidemic.*
Nonlinear Analysis: Real World Applications, 14 (3).
pp. 1434-1456.
ISSN 1468-1218

Lu, Y. and Zhang, L and Mao, Xuerong
(2013)
*Distributed information consensus filters for simultaneous input and state estimation.*
Circuits, Systems, and Signal Processing, 32 (2).
pp. 877-888.
ISSN 1531-5878

Higham, Desmond and Mao, Xuerong and Roj, Mikolaj and Song, Qingshuo and Yin, George
(2013)
*Mean exit times and the multilevel Monte Carlo method.*
SIAM/ASA Journal on Uncertainty Quantification (JUQ), 1 (1).
pp. 2-18.

Mao, Xuerong and Szpruch, Lukasz
(2013)
*Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients.*
Stochastics: An International Journal of Probability and Stochastic Processes, 85 (1).
pp. 144-171.
ISSN 1744-2508

Wu, Fuke and Mao, Xuerong and Kloeden, Peter E.
(2013)
*Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations.*
Discrete and Continuous Dynamical Systems - Series A, 33 (2).
pp. 885-903.
ISSN 1078-0947

Hu, Liangjian and Mao, Xuerong and Shen, Yi
(2013)
*Stability and boundedness of nonlinear hybrid stochastic differential delay equations.*
Systems and Control Letters, 62 (2).
pp. 178-187.
ISSN 0167-6911

Mao, Xuerong and Szpruch, Lukasz
(2013)
*Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients.*
Journal of Computational and Applied Mathematics, 238.
pp. 14-28.
ISSN 0377-0427

Mao, Wei and Mao, Xuerong
(2013)
*Approximate solutions of hybrid stochastic pantograph equations with Levy jumps.*
Abstract and Applied Analysis, 2013.

Mao, Xuerong and Sabanis, Sotirios
(2013)
*Delay geometric Brownian motion in financial option valuation.*
Stochastics: An International Journal of Probability and Stochastic Processes, 85 (2).
pp. 295-320.
ISSN 1744-2508

Hu, Junhao and Mao, Xuerong and Yuan, Chenggui
(2013)
*Razumikhin-type theorems on exponential stability of SDDEs containing singularly perturbed random processes.*
Abstract and Applied Analysis, 2013.

Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng
(2012)
*The SIS epidemic model with Markovian switching.*
Journal of Mathematical Analysis and Applications, 394 (2).
pp. 496-516.
ISSN 0022-247X

Baduraliya, Chaminda and Mao, Xuerong
(2012)
*The Euler-Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model.*
Computers and Mathematics with Applications, 64 (7).
pp. 2209-2223.
ISSN 0898-1221

Deng, Feiqi and Luo, Qi and Mao, Xuerong
(2012)
*Stochastic stabilization of hybrid differential equations.*
Automatica, 48 (9).
pp. 2321-2328.
ISSN 0005-1098

Li, Xiaoyue and Mao, Xuerong
(2012)
*A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching ☆.*
Automatica, 48 (9).
pp. 2329-2334.
ISSN 0005-1098

Nguyen, Dung Tien and Mao, Xuerong and Yin, G. and Yuan, Chenggui
(2012)
*Stability of singular jump-linear systems with a large state space : a two-time-scale approach.*
The Australian and New Zealand Industrial and Applied Mathematics Journal, 52 (4).
pp. 372-390.

Bao, J. H. and Mao, X. R. and Yuan, C. G.
(2012)
*Lyapunov exponents of hybrid stochastic heat equations.*
Systems and Control Letters, 61 (1).
pp. 165-172.
ISSN 0167-6911

Li, Chanying and Chen, Michael Z.Q. and Lam, J. and Mao, Xuerong
(2012)
*On exponentially almost sure stability of random jump systems.*
IEEE Transactions on Automatic Control, 57 (12).
pp. 3064-3077.
ISSN 0018-9286

Li, Xiaoyue and Mao, Xuerong
(2012)
*The improved LaSalle-type theorems for stochastic differential delay equations.*
Stochastic Analysis and Applications, 30 (4).
pp. 568-589.
ISSN 0736-2994

Bao, Jianhai and Mao, Xuerong and Yin, George and Yuan, Chenggui
(2011)
*Competitive Lotka-Volterra population dynamics with jumps.*
Nonlinear Analysis: Theory, Methods and Applications, 74 (17).
pp. 6601-6616.
ISSN 0362-546X

Bao, Jianhai and Mao, Xuerong and Yin, Geroge and Yuan, Chenggui
(2011)
*Competitive Lotka–Volterra population dynamics with jumps.*
Nonlinear Analysis: Theory, Methods and Applications, 74 (17).
pp. 6601-6616.
ISSN 0362-546X

Bao, Jianhai and Bottcher, Bjorn and Mao, Xuerong and Yuan, Chenggui
(2011)
*Convergence rate of numerical solutions to SFDEs with jumps.*
Journal of Computational and Applied Mathematics, 236 (2).
pp. 119-131.
ISSN 0377-0427

Szpruch, Lukasz and Mao, Xuerong and Higham, Desmond J. and Pan, Jiazhu
(2011)
*Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model.*
BIT Numerical Mathematics, 51.
pp. 405-425.
ISSN 0006-3835

Mao, Xuerong
(2011)
*Stationary distribution of stochastic population systems.*
Systems and Control Letters, 60 (6).
pp. 398-405.
ISSN 0167-6911

Vass, J. Keith and Higham, D.J. and Mudaliar, Manikhandan A V and Mao, Xuerong and Crowther, D.J.
(2011)
*Discretization provides a conceptually simple tool to build expression networks.*
PLoS One, 6 (4).
e18634.
ISSN 1932-6203

Li, Xiaoyue and Gray, Alison and Jiang, Daqing and Mao, Xuerong
(2011)
*Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching.*
Journal of Mathematical Analysis and Applications, 376 (1).
pp. 11-28.
ISSN 0022-247X

Higham, Desmond J. and Intep, Somkid and Mao, Xuerong and Szpruch, Lukasz
(2011)
*Hybrid simulation of autoregulation within transcription and translation.*
BIT Numerical Mathematics, 51 (1).
pp. 177-196.
ISSN 0006-3835

Mao, Xuerong
(2011)
*Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions.*
Applied Mathematics and Computation, 217 (12).
pp. 5512-5524.
ISSN 0096-3003

Huang, Lirong and Mao, Xuerong
(2011)
*Stability of singular stochastic systems with Markovian switching.*
IEEE Transactions on Automatic Control, 56 (2).
pp. 424-429.
ISSN 0018-9286

Mao, Xuerong and Shen, Yi and Gray, Alison
(2011)
*Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations.*
Journal of Computational and Applied Mathematics, 235 (5).
pp. 1213-1226.
ISSN 0377-0427

Wu, Fuke and Mao, Xuerong and Kloeden, Peter E.
(2011)
*Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations.*
Random Operator and Stochastic Equations, 19 (2).
pp. 105-216.
ISSN 0926-6364

Luo, Qi and Mao, Xuerong and Shen, Yi
(2011)
*Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations.*
Automatica, 47.
pp. 2075-2081.
ISSN 0005-1098

Wu, Fuke and Hu, Shigeng and Mao, Xuerong
(2011)
*Razumikhin-type theorem for neutral stochastic functional differential equations with unbounded delay.*
Acta Mathematica Scientia, 31B (4).
pp. 1245-1258.

Gray, Alison and Greenhalgh, David and Hu, L. and Mao, Xuerong and Pan, Jiafeng
(2011)
*A stochastic differential equation SIS epidemic model.*
SIAM Journal on Applied Mathematics, 71 (3).
pp. 876-902.

Wu, Fuke and Mao, Xuerong and Szpruch, Lukasz
(2010)
*Almost sure exponential stability of numerical solutions for stochastic delay differential equations.*
Numerische Mathematik, 115 (4).
pp. 681-697.

Huang, Lirong and Mao, Xuerong
(2010)
*On almost sure stability of hybrid stochastic systems with mode-dependent interval delays.*
IEEE Transactions on Automatic Control, 55 (8).
pp. 1946-1952.
ISSN 0018-9286

Li, Xiaoyue and Mao, Xuerong and Shen, Yi
(2010)
*Approximate solutions of stochastic differential delay equations with Markovian switching.*
Journal of Difference Equations and Applications, 16 (2-3).
pp. 195-207.
ISSN 1023-6198

Huang, Lirong and Mao, Xuerong
(2010)
*SMC design for robust H∞ control of uncertain stochastic delay systems.*
Automatica, 46 (2).
pp. 405-412.
ISSN 0005-1098

Yin, G. and Mao, X. and Yuan, C. and Cao, D.
(2010)
*Approximation methods for hybrid diffusion systems with state-dependent switching processes : numerical algorithms and existence and uniqueness of solutions.*
SIAM Journal on Mathematical Analysis, 41 (6).
pp. 2335-2352.
ISSN 0036-1410

Appleby, John A.D. and Mao, Xuerong and Wu, H.
(2010)
*On the almost sure running maxima of solutions of affine stochastic functional differential equations.*
SIAM Journal on Mathematical Analysis, 42 (2).
pp. 646-678.
ISSN 0036-1410

Appleby, John A.D. and Kelly, C. and Mao, Xuerong and Rodkina, A.
(2010)
*On the local dynamics of polynomial difference equations with fading stochastic perturbations.*
Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis, 17.
pp. 401-430.
ISSN 1201-3390

Huang, Lirong and Mao, Xuerong and Deng, Feiqi
(2009)
*Delay-dependent robust stability of stochastic delay systems with Markovian switching.*
Journal of Control Theory and Applications, 7 (4).
pp. 367-372.
ISSN 1672-6340

Giles, Michael B. and Higham, Desmond J. and Mao, Xuerong
(2009)
*Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff.*
Finance and Stochastics, 13 (3).
pp. 403-413.
ISSN 0949-2984

Dalal, Nirav and Greenhalgh, David and Mao, Xuerong,
University of Strathclyde (Funder)
(2009)
*Mathematical modelling of internal HIV dynamics.*
Discrete and Continuous Dynamical Systems - Series B, 12 (2).
pp. 305-321.
ISSN 1531-3492

Hu, Guangda and Liu, Mingzhu and Mao, Xuerong and Song, Minghui,
National Natural Science Foundation of China (Funder), University of Science and Technology, Beijing (Funder), Harbin Institute of Technology (Funder)
(2009)
*Noise expresses exponential growth under regime switching.*
Systems and Control Letters, 58 (9).
pp. 691-699.
ISSN 0167-6911

Mao, X. and Hu, G. and Liu, M. and Song, M.,
National Natural Science Foundation of China (Funder), London Mathematical Society (Funder), Royal Society of Edinburgh (Funder), Harbin Institute of Technology. (Funder), University of Science and Technology Beijing (Funder)
(2009)
*Noise suppresses exponential growth under regime switching.*
Journal of Mathematical Analysis and Applications, 355 (2).
pp. 783-795.
ISSN 0022-247X

Luo, Q. and Mao, Xuerong,
National Natural Science Foundation of China (Funder), EPSRC (UK) (Funder), London Mathematical Society (Funder), Edinburgh Mathematical Society (Funder)
(2009)
*Stochastic population dynamics under regime switching II.*
Journal of Mathematical Analysis and Applications, 355 (2).
pp. 577-593.
ISSN 0022-247X

Huang, L.R. and Mao, X.R.
(2009)
*Delay-dependent exponential stability of neutral stochastic delay systems (vol 54, pg 147, 2009).*
IEEE Transactions on Automatic Control, 54 (7).
p. 1733.
ISSN 0018-9286

Mao, X. and Appleby, J. and Lynch, T. and Wu, H.
(2009)
*The size of the largest fluctuations in a market model with Markovian switching.*
Communications in Applied Analysis, 13 (2).
pp. 135-166.
ISSN 1083-2564

Huang, L. and Mao, X.
(2009)
*Delay-dependent exponential stability of neutral stochastic delay systems.*
IEEE Transactions on Automatic Control, 54 (1).
pp. 147-152.
ISSN 0018-9286

Mao, X. and Yin, J. and Wu, F.
(2009)
*Generalized stochastic delay Lotka-Volterra systems.*
Stochastic Models, 25 (3).
pp. 436-454.
ISSN 1532-6349

Appleby, John A. D. and Mao, Xuerong and Riedle, Markus
(2009)
*Geometric Brownian motion with delay : mean square characterisation.*
Proceedings of the American Mathematical Society, 137 (1).
pp. 339-348.
ISSN 0002-9939

Huang, Lirong and Mao, Xuerong
(2009)
*On input-to-state stability of stochastic retarded systems with Markovian switching.*
IEEE Transactions on Automatic Control, 54 (8).
pp. 1898-1902.
ISSN 0018-9286

Li, Xiaoyue and Jiang, Daqing and Mao, Xuerong,
National Natural Science Foundation of China (Funder), Royal Society of Edinburgh (Funder)
(2009)
*Population dynamical behavior of Lotka-Volterra system under regime switching.*
Journal of Computational and Applied Mathematics, 232 (2).
pp. 427-448.
ISSN 0377-0427

Li, X. and Mao, X.,
National Natural Science Foundation of China (Funder), Key Project of Chinese Ministry of Education (Funder), Key Laboratory for Applied Statistics of MOE (KLAS) (Funder)
(2009)
*Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation.*
Discrete and Continuous Dynamical Systems - Series A, 24 (2).
pp. 523-593.
ISSN 1078-0947

Intep, Somkid and Higham, Desmond J. and Mao, X.
(2009)
*Switching and diffusion models for gene regulation networks.*
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8 (1).
pp. 30-45.
ISSN 1540-3459

Wu, Fuke and Mao, Xuerong and Chen, Kan,
Chinese Scholarship Council (Funder)
(2008)
*A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations.*
Journal of Mathematical Analysis and Applications, 348 (1).
pp. 540-554.
ISSN 0022-247X

Yin, Juliang and Mao, Xuerong,
NSF of Guangdong Province (Funder)
(2008)
*The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications.*
Journal of Mathematical Analysis and Applications, 346 (2).
pp. 345-358.
ISSN 0022-247X

Mao, Xuerong and Shen, Yi and Yuan, Chenggui,
EPSRC (U.K.) (Funder), National Natural Science Foundation of China (Funder)
(2008)
*Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching.*
Stochastic Processes and their Applications, 118 (8).
pp. 1385-1406.
ISSN 0304-4149

Mao, Xuerong and Lam, James and Huang, Lirong,
RGC HKU 7029/05P. (Funder)
(2008)
*Stabilisation of hybrid stochastic differential equations by delay feedback control.*
Systems and Control Letters, 57 (11).
pp. 927-935.
ISSN 0167-6911

Wu, Fuke and Mao, Xuerong and Yin, Juliang
(2008)
*Uncertainty and economic growth in a stochastic R&D model.*
Economic Modelling, 25 (6).
pp. 1306-1317.
ISSN 0264-9993

Dalal, N. and Greenhalgh, D. and Mao, X.
(2008)
*A stochastic model for internal HIV dynamics.*
Journal of Mathematical Analysis and Applications, 341 (2).
pp. 1084-1101.
ISSN 0022-247X

Wu, Fuke and Mao, Xuerong,
Chinese Scholarship Council (Funder)
(2008)
*Numerical solutions of neutral stochastic functional differential equations.*
SIAM Journal on Numerical Analysis, 46 (4).
pp. 1821-1841.
ISSN 0036-1429

Appleby, John A. D. and Mao, Xuerong and Rodkina, Alexandra
(2008)
*Stabilisation and destabilisation of nonlinear differential equations by noise.*
IEEE Transactions on Automatic Control, 53 (3).
pp. 683-691.
ISSN 0018-9286

Pang, Sulin and Deng, Feiqi and Mao, Xuerong,
EPSRC (Funder), National Science Foundation of China (Funder), Jinan University of China (Funder)
(2008)
*Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations.*
Journal of Computational and Applied Mathematics, 213 (1).
pp. 127-141.
ISSN 0377-0427

Yang, Zhe and Mao, Xuerong and Yuan, Chenggui
(2008)
*Comparison theorem of one-dimensional stochastic hybrid delay systems.*
Systems and Control Letters, 57 (1).
pp. 56-63.

Hu, Liangjian and Mao, Xuerong
(2008)
*Almost sure exponential stabilisation of stochastic systems by state-feedback control.*
Automatica, 44 (2).
pp. 465-471.
ISSN 0005-1098

Pang, S. and Deng, F. and Mao, X.,
EPSRC (U.K.) (Funder), National Natural Science Foundation of China (Funder), Key Programs of Science and Technology of Guangzhou (Funder), Jinan University of China (Funder)
(2008)
*Asymptotic properties of stochastic population dynamics.*
Dynamics of Continuous Discrete and Impulsive Systems Series A: Mathematical Analysis, 15 (5a).
pp. 603-620.
ISSN 1201-3390

Deng, Feiqi and Luo, Qi and Mao, Xuerong and Pang, Sulin,
EPSRC (Funder), National Natural Science Foundation of China (Funder), Key Programs of Science and Technology of Guangzhou (Funder), Jinan Universit of China (Funder)
(2008)
*Noise suppresses or expresses exponential growth.*
Systems and Control Letters, 57 (3).
pp. 262-270.
ISSN 0167-6911

Huang, Lirong and Mao, Xuerong and Deng, Feiqi
(2008)
*Stability of hybrid stochastic retarded systems.*
IEEE Transactions on Circuits and Systems I: Regular Papers, 55 (11).
pp. 3413-3420.
ISSN 1549-8328

Mao, X. and Luo, Q. and Deng, F. and Bao, J. and Zhang, Y.
(2008)
*Theory and application of stability for stochastic reaction diffusion systems.*
Science in China Series F - Information Sciences, 51 (2).
pp. 158-170.
ISSN 1009-2757

Mao, X. and Yuan, C.
(2008)
*A note on the rate of convergence of the Euler-Maruyama method for stochastic differential equations.*
Stochastic Analysis and Applications, 26 (2).
pp. 325-333.
ISSN 0736-2994

Xu, Shengyuan and Lam, James and Mao, Xuerong
(2007)
*Delay-dependent H∞ control and filtering for uncertain Markovian jump systems with time-varying delays.*
IEEE Transactions on Circuits and Systems I: Regular Papers, 54 (9).
pp. 2070-2077.
ISSN 1057-7122

Higham, D.J. and Mao, X. and Yuan, C.
(2007)
*Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations.*
SIAM Journal on Numerical Analysis, 45 (2).
pp. 592-609.
ISSN 0036-1429

Luo, Qi and Mao, Xuerong and Shen, Yi
(2006)
*New criteria on exponential stability of neutral stochastic differential delay equations.*
Systems and Control Letters, 55 (10).
pp. 826-834.
ISSN 0167-6911

Shen, Yi and Mao, Xuerong
(2006)
*Asymptotic behaviours of stochastic differential delay equations.*
Asian Journal of Control, 8 (1).
21–27.
ISSN 1561-8625

Mao, X. and Yuan, C. and Zou, J.
(2005)
*Stochastic differential delay equations of population dynamics.*
Journal of Mathematical Analysis and Applications, 304 (1).
pp. 296-320.
ISSN 0022-247X

Mao, X. and Yuan, C. and Yin, G.
(2005)
*Numerical method for stationary distribution of stochastic differential equations with Markovian switching.*
Journal of Computational and Applied Mathematics, 174 (1).
pp. 1-27.
ISSN 0377-0427

Higham, D.J. and Mao, X.
(2005)
*Convergence of Monte Carlo simulations involving the mean-reverting square root process.*
Journal of Computational Finance, 8 (3).
pp. 35-61.
ISSN 1460-1559

Bahar, Arifah and Mao, Xuerong
(2004)
*Stochastic delay Lotka-Volterra model.*
Journal of Mathematical Analysis and Applications, 292 (2).
pp. 364-380.
ISSN 0022-247X

Yuan, Chenggui and Mao, Xuerong
(2004)
*Robust stability and controllability of stochastic differential delay equations with Markovian switching.*
Automatica, 40 (3).
pp. 343-354.
ISSN 0005-1098

Higham, D.J. and Mao, X. and Stuart, A.M.
(2003)
*Exponential mean square stability of numerical solutions to stochastic differential equations.*
LMS Journal of Computation and Mathematics, 6.
pp. 297-313.
ISSN 1461-1570

Mao, Xuerong and Sabanis, Sotirios and Renshaw, Eric
(2003)
*Asymptotic behaviour of the stochastic Lotka-Volterra model.*
Journal of Mathematical Analysis and Applications, 287 (1).
pp. 141-156.
ISSN 0022-247X

Yuan, Chenggui and Mao, Xuerong
(2003)
*Asymptotic stability in distribution of stochastic differential equations with Markovian switching.*
Stochastic Processes and their Applications, 103 (2).
pp. 277-291.
ISSN 0304-4149

Mao, X.
(2003)
*Numerical solutions of stochastic functional differential equations.*
LMS Journal of Computation and Mathematics, 6.
pp. 141-161.
ISSN 1461-1570

Mao, X.
(2002)
*Exponential stability of stochastic delay interval systems with Markovian switching.*
IEEE Transactions on Automatic Control, 47 (10).
pp. 1604-1612.
ISSN 0018-9286

Mao, X.
(2002)
*A note on the LaSalle-type theorems for stochastic differential delay equations.*
Journal of Mathematical Analysis and Applications, 268 (1).
pp. 125-142.
ISSN 0022-247X

Mao, Xuerong and Marion, Glenn and Renshaw, Eric
(2002)
*Environmental Brownian noise suppresses explosions in population dynamics.*
Stochastic Processes and their Applications, 97 (1).
pp. 95-110.
ISSN 0304-4149

Higham, D.J. and Mao, X. and Stuart, A.M.
(2002)
*Strong convergence of Euler-type methods for nonlinear stochastic differential equations.*
SIAM Journal on Numerical Analysis, 40 (3).
pp. 1041-1063.
ISSN 0036-1429

Blythe, Steve and Mao, Xuerong and Liao, Xiaoxin
(2001)
*Stability of stochastic delay neural networks.*
Journal of the Franklin Institute, 338 (4).
pp. 481-495.
ISSN 0016-0032

Mao, X.
(1999)
*Stochastic versions of the LaSalle theorem.*
Journal of Differential Equations, 153 (1).
pp. 175-195.
ISSN 0022-0396

Mao, Xuerong
(1999)
*Stability of stochastic differential equations with Markovian switching.*
Stochastic Processes and their Applications, 79 (1).
pp. 45-67.
ISSN 0304-4149

Mao, Xuerong and Koroleva, Natalia and Rodkina, Alexandra
(1998)
*Robust stability of uncertain stochastic differential delay equations.*
Systems and Control Letters, 35 (5).
pp. 325-336.
ISSN 0167-6911

Mao, Xuerong
(1997)
*Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations.*
SIAM Journal on Mathematical Analysis, 28 (2).
pp. 389-401.
ISSN 0036-1410

Mao, Xuerong
(1996)
*Razumikhin-type theorems on exponential stability of stochastic functional differential equations.*
Stochastic Processes and their Applications, 65 (2).
pp. 233-250.
ISSN 0304-4149

Mao, X.
(1996)
*Robustness of exponential stability of stochastic differential delay equations.*
IEEE Transactions on Automatic Control, 41 (3).
pp. 442-447.
ISSN 0018-9286

Mao, Xuerong
(1995)
*Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients.*
Stochastic Processes and their Applications, 58 (2).
pp. 281-292.
ISSN 0304-4149

Mao, Xuerong
(1994)
*Stochastic stabilization and destabilization.*
Systems and Control Letters, 23 (4).
pp. 279-290.
ISSN 0167-6911

## Conference or Workshop Item

Gray, Alison and Pan, Jiafeng and Greenhalgh, David and Mao, Xuerong
(2015)
*Parameter estimation for the stochastic SIS epidemic model.*
In: 26th Numerical Analysis Conference, 2015-06-23 - 2015-06-26, University of Strathclyde.
(Unpublished)

Greenhalgh, David and Gray, Alison and Mao, Xuerong and Pan, Jiafeng
(2012)
*Limiting behaviour of an SIS epidemic model with environmental stochasticity.*
In: 13th WSEAS International Conference on Mathematics and Computers in Biology and Chemistry, 2012-06-13 - 2012-09-15.
(Unpublished)

Pan, Jiafeng and Gray, Alison and Greenhalgh, David and Mao, Xuerong
(2012)
*Estimation of parameters for the SDE SIS epidemic model.*
In: Workshop on Stochastic Modelling in Ecosystems, 2012-06-11 - 2012-06-12.
(Unpublished)

Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng
(2012)
*SDE SIS epidemic models.*
In: Workshop on Stochastic Modelling in Ecosystems, 2012-06-11 - 2012-06-12.
(Unpublished)

## Book

Mao, Xuerong
(2007)
*Stochastic differential equations and applications.*
Elsevier.
ISBN 9781904275343

Mao, X. and Yuan, C.
(2006)
*Stochastic differential equations with Markovian switching.*
Imperial College Press.
ISBN 9781860947018

Mao, Xuerong
(1997)
*Stochastic Differential Equations and Applications.*
Horwood.
ISBN 1898563268

Mao, Xuerong
(1994)
*Exponential stability of stochastic differential equations.*
Marcel Dekker.
ISBN 0824790804

Mao, X
(1991)
*Stability of Stochastic Differential Equations with Respect to Semimartingales.*
Pitman research notes in mathematics series
.
Longman.
ISBN 9780582080362

**Sat Feb 17 07:20:53 2018 GMT**.