The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations

摘要

This paper develops the partially truncated Euler–Maruyama method for a class of highly nonlinear pantograph stochastic differential equations under the generalized Khasminskii-type conditions. The order of Lp-convergence is obtained. Moreover, some almost sure polynomial stability and mean square polynomial stability criteria are established for the numerical solution. Numerical examples are provided to illustrate the theoretical results.