Mean square convergence of explicit two-step methods for highly nonlinear stochastic differential equations

Jingjun Zhao, Yulian Yi and Yang Xu

Applied Mathematics and Computation, 2019, vol. 361, issue C, 466-483

Abstract: In this paper, we propose the projected two-step Euler Maruyama method and the projected two-step Milstein method for highly nonlinear stochastic differential equations. Under a global monotonicity condition, we first examine the strong convergence (in mean square sense) for these two explicit schemes based on the notions of stochastic stability and B-consistency for two-step methods. We prove that the convergence rates of the projected two-step Euler Maruyama method and the projected two-step Milstein method are 12 and 1, respectively. In particular, our results can be applied to equations with super-linearly growing drift and diffusion coefficients. Finally, we numerically verify the optimal mean square convergence orders of these two schemes by a series of examples.

Keywords: Stochastic differential equation; Strong convergence; Two-step Euler Maruyama method; Two-step Milstein method; Global monotonicity condition (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319304394
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:466-483

DOI: 10.1016/j.amc.2019.05.037

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().