Explicit Milstein schemes with truncation for nonlinear stochastic differential equations: Convergence and its rate

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:374

Article

Li, Xiaoyue¹  Yin, George² 

[1] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China

[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

关键词: Explicit scheme;    Milstein method;    Polynomial growth;    Convergence rate;   

DOI  :  10.1016/j.cam.2020.112771

来源: Elsevier

【 摘 要 】

Although some implicit numerical procedures have been developed to treat high nonlinearity, the question whether one can use explicit schemes to achieve convergence rate similar to that of Milstein's procedure remained open. This brings us to the current work that focuses on numerical solutions of stochastic differential equations using explicit schemes. Our main goals are to obtain order one convergence in the second moment in a finite-time interval. In contrast to the implicit schemes, explicit schemes are advantageous, easily implementable, and computationally less intensive. To overcome the difficulties due to super-linear growth of the coefficients, a truncation device is used in our algorithm. In addition to reaching aforementioned goals in the analysis part, numerical examples are provided to demonstrate our results. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free