Mean-square stability of two classes of \(\theta \)-methods for neutral stochastic delay integro-differential equations. (English) Zbl 1450.65003
Summary: The mean-square stability of the \(\theta \)-method for neutral stochastic delay integro-differential equations (NSDIDEs) is considered in this paper. We construct two classes of \(\theta \)-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.
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 35R11 | Fractional partial differential equations |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
Keywords:
stochastic delay integro-differential equations; stochastic SLT and SST methods; mean-square exponential stabilityReferences:
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