Convergence and Stability of Split-Step Milstein Schemes for Stochastic Differential Equations
Lingzhi Teng *
College of Science, Guilin University of Technology, Guilin 541004, Guangxi, P.R. China.
Haomin Zhang
College of Science, Guilin University of Technology, Guilin 541004, Guangxi, P.R. China.
Xiaoting Tao
College of Science, Guilin University of Technology, Guilin 541004, Guangxi, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the mean square convergence and stability of the split-step theta-Milstein schemes for stochastic differential equations are discussed. First, it is shown that these methods are mean square convergent with strong order 1. Then, we investigate the mean square stability of the split-step theta-Milstein methods. Finally, numerical examples are presented to illustrate the theoretical results.
Keywords: Stochastic differential equations, Mean square convergence, Mean square stability, Split-step theta-Milstein schemes.