Volume 38, Issue 6
Convergence Rate of the Truncated Euler-Maruyama Method for Neutral Stochastic Differential Delay Equations with Markovian Switching

J. Comp. Math., 38 (2020), pp. 903-932.

Published online: 2020-06

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• Abstract

The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition. We also study its strong convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are given to illustrate the theoretical results.

• Keywords

Neutral stochastic differential delay equations, Truncated Euler-Maruyama method, Local Lipschitz condition, Khasminskii-type condition, Markovian switching.

• AMS Subject Headings

65L20, 65C40

weizhanghlj@163.com (Wei Zhang)

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@Article{JCM-38-903, author = {Zhang , Wei }, title = {Convergence Rate of the Truncated Euler-Maruyama Method for Neutral Stochastic Differential Delay Equations with Markovian Switching}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {6}, pages = {903--932}, abstract = {

The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition. We also study its strong convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are given to illustrate the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2018-0237}, url = {http://global-sci.org/intro/article_detail/jcm/16973.html} }
TY - JOUR T1 - Convergence Rate of the Truncated Euler-Maruyama Method for Neutral Stochastic Differential Delay Equations with Markovian Switching AU - Zhang , Wei JO - Journal of Computational Mathematics VL - 6 SP - 903 EP - 932 PY - 2020 DA - 2020/06 SN - 38 DO - http://doi.org/10.4208/jcm.1906-m2018-0237 UR - https://global-sci.org/intro/article_detail/jcm/16973.html KW - Neutral stochastic differential delay equations, Truncated Euler-Maruyama method, Local Lipschitz condition, Khasminskii-type condition, Markovian switching. AB -

The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition. We also study its strong convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are given to illustrate the theoretical results.

Wei Zhang. (2020). Convergence Rate of the Truncated Euler-Maruyama Method for Neutral Stochastic Differential Delay Equations with Markovian Switching. Journal of Computational Mathematics. 38 (6). 903-932. doi:10.4208/jcm.1906-m2018-0237
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