High-order split-step theta methods for non-autonomous stochastic differential equations with non-globally Lipschitz continuous coefficients

摘要

In this paper, we first propose the so-called improved split-step theta methods for non-autonomous stochastic differential equations driven by non-commutative noise. Then, we prove that the improved split-step theta method is convergent with strong order of one for stochastic differential equations with the drift coefficient satisfying a superlinearly growing condition and a one-sided Lipschitz continuous condition. Finally, the obtained results are verified by numerical experiments. Copyright (C) 2016 John Wiley & Sons, Ltd.