Mean-square stability of two classes of [formula omitted]-methods for neutral stochastic delay integro-differential equations

Abstract

The mean-square stability of the θ-method for neutral stochastic delay integro-differential equations (NSDIDEs) is considered in this paper. We construct two classes of θ-methods, i.e. the stochastic linear theta (SLT) method and the split-step theta (SST) method for NSDIDEs. Under the one-sided growth condition and contractive condition, we show that both methods are mean-square exponentially stable. An example is given to illustrate the theoretical results.