Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations
We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When θ ≥ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h > 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.
Keywordsstochastic differential equations mean-square stability improved split-step theta methods exponential mean-square stability
MSC(2010)65C20 65L20 60H35
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This work was supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11371157) and the Scientific Research Innovation Team of the University “Aviation Industry Economy” (Grant No. 2016TD02). The author thanks the referees for their valuable comments and suggestions.
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