Strong convergence and exponential stability of stochastic differential equations with piecewise continuous arguments for non-globally Lipschitz continuous coefficients

摘要

The paper deals with a split-step θ-method for stochastic differential equations with piecewise continuous arguments (SEPCAs). The strong convergence of the method is proved under non-globally Lipschitz conditions. The exponential stability of the exact and numerical solutions is obtained. Some experiments are given to illustrate the conclusions.