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In this paper, the backward Euler (BE) method is introduced and analyzed for linear neutral hybrid stochastic delay differential equations. The exponential mean square stability of the BE method is considered for linear neutral hybrid stochastic delay differential equations. It is proved that, under the one-sided Lipschitz condition and the linear growth condition, for some positive stepsizes which depend on the Markovian switching, the BE method is exponential mean square stable. A numerical example is provided to illustrate the theoretical results.

Exponential Mean Square Stability of the BE Method for Linear Neutral Hybrid Stochastic Delay Differential Equations