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

Wei Mao, Xuerong Mao

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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.
Original languageEnglish
Pages (from-to)104-119
Number of pages16
JournalApplied Mathematics and Computation
Early online date18 Jan 2014
Publication statusPublished - 1 Mar 2014


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

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