Approximate solutions for a class of doubly perturbed stochastic differential equations

Wei Mao, Liangjian Hu, Xuerong Mao

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4 Citations (Scopus)
13 Downloads (Pure)

Abstract

In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the Carathéodory approximate solution converges to the solution of DPSDEs under the global Lipschitz condition. Moreover, we extend the above results to the case of DPSDEs with non-Lipschitz coefficients.

Original languageEnglish
Number of pages17
JournalAdvances in Difference Equations
Volume2018
Issue number1
DOIs
Publication statusPublished - 24 Jan 2018

Keywords

  • Carathéodory approximate solution
  • doubly perturbed stochastic differential equations
  • global Lipschitz condition
  • non-Lipschitz condition

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