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

Wei Mao, Surong You, Xuerong Mao

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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
Original languageEnglish
JournalJournal of Computational and Applied Mathematics
Early online date21 Jan 2016
DOIs
Publication statusPublished - 1 Aug 2016

Keywords

  • asymptotic stability
  • numerical analysis

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