Discrete-time approximations of stochastic delay equations: The Milstein scheme

• 成果类型: Article
• 署名作者: Hu, YZ; Mohammed, SEA; Yan, F
• 署名单位: University of Kansas; Southern Illinois University System; Southern Illinois University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2004
• 页码: 265-314
• 关键词: integrals; extension; calculus; FORMULA

摘要

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Ito formula for tame functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the nonanticipating nature of the SDDE, the use of anticipating calculus methods in the context of strong approximation schemes appears to be novel.