Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902070 | Journal of Computational and Applied Mathematics | 2018 | 33 Pages |
Abstract
This paper examines convergence and stability of the two classes of theta-Milstein schemes for stochastic differential equations (SDEs) with non-global Lipschitz continuous coefficients: the split-step theta-Milstein (SSTM) scheme and the stochastic theta-Milstein (STM) scheme. For θâ[1â2,1], this paper concludes that the two classes of theta-Milstein schemes converge strongly to the exact solution with the order 1. For θâ[0,1â2], under the additional linear growth condition for the drift coefficient, these two classes of the theta-Milstein schemes are also strongly convergent with the standard order. This paper also investigates exponential mean-square stability of these two classes of the theta-Milstein schemes. For θâ(1â2,1], these two theta-Milstein schemes can share the exponential mean-square stability of the exact solution. For θâ[0,1â2], similar to the convergence, under the additional linear growth condition, these two theta-Milstein schemes can also reproduce the exponential mean-square stability of the exact solution.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Xiaofeng Zong, Fuke Wu, Guiping Xu,