On delay-dependent exponential stability of the split-step backward euler method for stochastic delay differential equations

Abstract

This paper investigates the delay-dependent stability of the split-step backward Euler method for nonlinear stochastic delay differential equations. Under a delay-dependent stability condition, in the case of fixed stepsize, it is proved that the split-step backward Euler method can reproduce the mean-square exponential stability of the exact solution under the restriction on the stepsize. Numerical experiments are also provided for demonstration.