Mean-square stability of two classes of θ-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.

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