Stability of stochastic θ-methods for stochastic delay integro-differential equations

Abstract

In this paper, we are concerned with the numerical stability of linear stochastic delay integro-differential equations (SDIDEs). A sufficient condition for mean square stability of the exact solution of a linear SDIDE with multiplicative noise is derived. Then the mean square stability of stochastic θ-methods is investigated, and it is shown that the numerical solution can reproduce the mean square stability of the exact solution under appropriate conditions. At last, we present some numerical experiments to support our conclusions.