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Volume 14, Issue 1
Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments

Yidan Geng, Minghui Song, Yulan Lu & Mingzhu Liu

DOI: 10.4208/nmtma.OA-2019-0108

Numer. Math. Theor. Meth. Appl., 14 (2021), pp. 194-218.

Published online: 2020-10

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  • Abstract

In this paper, we develop the truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The order of convergence is obtained. Moreover, we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs. Numerical examples are provided to support our conclusions.

  • Keywords

Stochastic differential equations with piecewise continuous argument, local Lipschitz condition, Khasminskii-type condition, truncated Euler-Maruyama method, convergence and stability.

  • AMS Subject Headings

65C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-14-194, author = {Geng , YidanSong , MinghuiLu , Yulan and Liu , Mingzhu}, title = {Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2020}, volume = {14}, number = {1}, pages = {194--218}, abstract = {

In this paper, we develop the truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The order of convergence is obtained. Moreover, we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs. Numerical examples are provided to support our conclusions.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0108}, url = {http://global-sci.org/intro/article_detail/nmtma/18332.html} }
TY - JOUR T1 - Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments AU - Geng , Yidan AU - Song , Minghui AU - Lu , Yulan AU - Liu , Mingzhu JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 194 EP - 218 PY - 2020 DA - 2020/10 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2019-0108 UR - https://global-sci.org/intro/article_detail/nmtma/18332.html KW - Stochastic differential equations with piecewise continuous argument, local Lipschitz condition, Khasminskii-type condition, truncated Euler-Maruyama method, convergence and stability. AB -

In this paper, we develop the truncated Euler-Maruyama (EM) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs), and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The order of convergence is obtained. Moreover, we show that the truncated EM method can preserve the exponential mean square stability of SDEPCAs. Numerical examples are provided to support our conclusions.

Geng , YidanSong , MinghuiLu , Yulan and Liu , Mingzhu. (2020). Convergence and Stability of the Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments. Numerical Mathematics: Theory, Methods and Applications. 14 (1). 194-218. doi:10.4208/nmtma.OA-2019-0108
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