EDGEWORTH EXPANSION FOR EULER APPROXIMATION OF CONTINUOUS DIFFUSION PROCESSES

• 成果类型: Article
• 署名作者: Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro
• 署名单位: Aarhus University; CREATES; Aarhus University; University of Tokyo
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1549
• 发表日期: 2020
• 页码: 1971-2003
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; ASYMPTOTIC-EXPANSION; CONVERGENCE; scheme

摘要

In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work (Stochastic Process. Appl. 123 (2013) 887-933), which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to the Euler scheme, and for studentized version of the error process.