TY - JOUR
T1 - The Convergence of Truncated Euler-Maruyama Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Generalized One-Sided Lipschitz Condition
AU - Geng , Yidan
AU - Song , Minghui
AU - Liu , Mingzhu
JO - Journal of Computational Mathematics
VL - 4
SP - 663
EP - 682
PY - 2023
DA - 2023/02
SN - 41
DO - http://doi.org/10.4208/jcm.2109-m2021-0116
UR - https://global-sci.org/intro/article_detail/jcm/21410.html
KW - Stochastic differential equations, Piecewise continuous argument, One-sided Lipschitz condition, Truncated Euler-Maruyama method.
AB - <p style="text-align: justify;">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.</p>