Asymptotic error for the Milstein scheme for SDEs driven by continuous semimartingales

• 成果类型: Article
• 署名作者: Yan, LQ
• 署名单位: State University System of Florida; University of Florida
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000520
• 发表日期: 2005
• 页码: 2706-2738
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; euler scheme

摘要

A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semi martingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SIDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumption on their finite variation part. The asymptotic behavior (weak convergence) of the normalized error processes was also studied.