On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps

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 (https://doi.org/10.1016/j.cam.2016.01.020)

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Abstract

This paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps. By the Itô formula, stochastic inequality and semi-martingale convergence theorem, we study the asymptotic stability in the pth moment and almost sure exponential stability of solutions under the local Lipschitz condition and nonlinear growth condition. On the other hand, we also show the convergence in probability of numerical schemes under nonlinear growth condition. Finally, an example is provided to illustrate the theory

ORCID iDs

Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864

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• Item metadata

  Item type:	Article
  ID code:	55488
  Dates:	Date Event 1 August 2016 Published 21 January 2016 Published Online 2 January 2016 Accepted
  Notes:	Accepted on 02/01/2016
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	08 Feb 2016 15:58
  Last modified:	02 Dec 2024 01:16
  URI:	https://strathprints.strath.ac.uk/id/eprint/55488