Strong Convergence of the Tamed Euler Method for Stochastic Differential Equations with Piecewise Continuous Arguments and Poisson Jumps under Non-globally Lipschitz Continuous Coefficients

Abstract

In the present work, the tamed Euler method is proven to be strongly convergent for stochastic differential equations with piecewise continuous arguments and Poisson jumps, where the diffusion and jump coefficients are global Lipschitz continuous, the drift coefficient is one-sided Lipschitz continuous, and its derivative demonstrates an at most polynomial growth. Moreover, the convergence rate is obtained.