摘要
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 0 ≥ 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.
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.
基金
supported by National Natural Science Foundation of China (Grant Nos. 91130003 and 11371157)
the Scientific Research Innovation Team of the University “Aviation Industry Economy” (Grant No. 2016TD02)
