Semi-tamed E–M Scheme for SDEs with Piecewise Continuous Arguments Driven by Poisson Jumps

The paper delves into numerical solution of stochastic differential equations with Poisson jumps and piecewise continuous arguments with superlinearly growing drift and diffusion coefficients. We assume that the drift and diffusion coefficients can be decomposed into two distinct parts. The first part is discretized using the classical Euler–Maruyama (E–M) scheme and the second part is discretized using the tamed E–M scheme. We provide a detailed analysis of the convergence rate for the semi-tamed E–M scheme. Two examples show that the semi-tamed approach achieves the same convergence rate, with a minor reduction in root mean square error and less computational effort, compared to fully tamed method.