Convergence of the Tamed Euler Method for Stochastic Differential Equations with Piecewise Continuous Arguments Under Non-global Lipschitz Continuous Coefficients. (4th April 2018)

• Record Type: Journal Article
• Authors: Song, M. H.; Lu, Y. L.; Liu, M. Z.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 5(2018)
• Page Start: 517
• Page End: 536
• Publication Date: 2018-04-04
• Subjects: Bounded in pth moment -- convergence order -- convergence -- stochastic differential equations with piecewise continuous arguments -- the tamed Euler method; 65C20 -- 60H35 -- 65L20; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1387862
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we deal with the strong convergence of numerical methods for stochastic differential equations with piecewise continuous arguments (SEPCAs) with at most polynomially growing drift coefficients and global Lipschitz continuous diffusion coefficients. An explicit and time-saving tamed Euler method is used to solve this type of SEPCAs. We show that the tamed Euler method is bounded in p th moment. And then the convergence of the tamed Euler method is proved. Moreover, the convergence order is one-half. Several numerical simulations are shown to verify the convergence of this method.