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

Abstract 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. [ABSTRACT FROM AUTHOR]