Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations |
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Authors: | Chao Yue |
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Institution: | 1.School of Economics and Trade,Zhengzhou University of Aeronautics,Zhengzhou,China |
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Abstract: | 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. |
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