High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients. (22nd February 2016)

• Record Type: Journal Article
• Authors: Yue, Chao
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 9(2016:Jun. 15)
• Page Start: 2380
• Page End: 2400
• Publication Date: 2016-02-22
• Subjects: stochastic differential equations -- one‐sided Lipschitz condition -- improved split‐step theta methods -- strong convergence -- superlinearly growing condition; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3647
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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 © 2016 John Wiley & Sons, Ltd.