@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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