A note on strong convergence of implicit scheme for SDEs under local one-sided Lipschitz conditions. Issue 2 (1st February 2021)

• Record Type: Journal Article
• Authors: Tan, Li; Yuan, Chenggui
• Is Part Of: International journal of computer mathematics. Volume 98:Issue 2(2021)
• Page Start: 238
• Page End: 251
• Publication Date: 2021-02-01
• Subjects: Stochastic differential equations -- implicit scheme -- local one-sided Lipschitz -- strong convergence -- discrete Gronwall inequality; 65C30 -- 65L20; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2020.1737861
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : In this paper, we aim to study strong convergence of theta-EM scheme for stochastic differential equations under a local one-sided Lipschitz condition. Since the existence and uniqueness of theta-EM solution cannot be guaranteed under the local one-sided Lipschitz condition, a modified theta-EM scheme is proposed, and strong convergence of the numerical solution to the exact solution is given.