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Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations

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

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Abstract

Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) (see e.g. Appleby and Reynolds (2008), Appleby and Rodkina (2009), Basin and Rodkina (2008), Khasminskii (1980), Mao (1995), Mao (1997), Mao (2007), Rodkina and Basin (2007), Shu, Lam, and Xu (2009), Yang, Gao, Lam, and Shi (2009), Yuan and Lygeros (2005) and Yuan and Lygeros (2006)). In general, the existing results on asymptotic stability and boundedness of SFDEs require (i) the coefficients of the SFDEs obey the local Lipschitz condition and the linear growth condition; (ii) the diffusion operator of the SFDEs acting on a C2,1-function be bounded by a polynomial with the same order as the C2,1-function. However, there are many SFDEs which do not obey the linear growth condition. Moreover, for such highly nonlinear SFDEs, the diffusion operator acting on a C2,1-function is generally bounded by a polynomial with a higher order than the C2,1-function. Hence the existing criteria on stability and boundedness for SFDEs are not applicable andwesee the necessity to develop new criteria. Our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up-bound for the diffusion operator may take a much more general form.

Item type: Article
ID code: 36919
Keywords: Brownian motion, stochastic theory, stochastic systems, stability analysis, stability criteria, boundedness, Probabilities. Mathematical statistics, Control and Systems Engineering, Electrical and Electronic Engineering
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Depositing user: Pure Administrator
Date Deposited: 20 Jan 2012 15:14
Last modified: 21 May 2015 14:17
Related URLs:
URI: http://strathprints.strath.ac.uk/id/eprint/36919

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