On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions

Wei Mao, Xuerong Mao

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we investigate the existence and uniqueness of solutions to neutral stochastic differential equations with Markovian switching and jumps (NSDEwMSJs) under non-Lipschitz conditions. On the other hand, we present the Euler approximate solutions for NSDEwMSJs and show that the convergence of the Euler approximate solutions to the true solutions by applying Itbo formula, Bihari’s lemma and Burkholder-Davis-Gundy’s lemma. Some examples are provided to illustrate the main results.
LanguageEnglish
Pages104-119
Number of pages16
JournalApplied Mathematics and Computation
Volume230
Early online date18 Jan 2014
DOIs
Publication statusPublished - 1 Mar 2014

Fingerprint

Markovian Switching
Non-Lipschitz
Stochastic Equations
Euler
Lemma
Jump
Approximate Solution
Differential equations
Differential equation
Approximation
Existence and Uniqueness of Solutions

Keywords

  • strong convergence
  • non-Lipschitz conditions
  • poisson random measure
  • Markovian switching
  • neutral SDEs

Cite this

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abstract = "In this paper, we investigate the existence and uniqueness of solutions to neutral stochastic differential equations with Markovian switching and jumps (NSDEwMSJs) under non-Lipschitz conditions. On the other hand, we present the Euler approximate solutions for NSDEwMSJs and show that the convergence of the Euler approximate solutions to the true solutions by applying Itbo formula, Bihari’s lemma and Burkholder-Davis-Gundy’s lemma. Some examples are provided to illustrate the main results.",
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