The Convergence of Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Generalized One-Sided Lipschitz Condition
Year: 2023
Author: Yidan Geng, Minghui Song, Mingzhu Liu
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 663–682
Abstract
In this paper, we consider the stochastic differential equations with piecewise continuous arguments (SDEPCAs) in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition. Since the delay term $t-[t]$ of SDEPCAs is not continuous and differentiable, the variable substitution method is not suitable. To overcome this difficulty, we adopt new techniques to prove the boundedness of the exact solution and the numerical solution. It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of $L^{\bar{q}}(\bar{q}\ge 2)$. We obtain the convergence order with some additional conditions. An example is presented to illustrate the analytical theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2109-m2021-0116
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 4 : pp. 663–682
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stochastic differential equations Piecewise continuous argument One-sided Lipschitz condition Truncated Euler-Maruyama method.
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