@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 = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2019-0108},
url = {http://global-sci.org/intro/article_detail/nmtma/18332.html}
}