@article{07eaae2c3f4f431d9cd519e73c1b6658,
title = "On the approximations of solutions to neutral SDEs with Markovian switching and jumps under non-Lipschitz conditions",
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{\textquoteright}s lemma and Burkholder-Davis-Gundy{\textquoteright}s lemma. Some examples are provided to illustrate the main results.",
keywords = "strong convergence, non-Lipschitz conditions, poisson random measure, Markovian switching, neutral SDEs",
author = "Wei Mao and Xuerong Mao",
note = "Notice: This is the author{\textquoteright}s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, Vol. 230 (01/03/2014) DOI: 10.1016/j.amc.2013.12.093",
year = "2014",
month = mar,
day = "1",
doi = "10.1016/j.amc.2013.12.093",
language = "English",
volume = "230",
pages = "104--119",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier Inc.",
}