EULER SCHEME FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTIONS: INTEGRABILITY AND CONVERGENCE IN LAW

• 成果类型: Article
• 署名作者: Leon, Jorge a.; Liu, Yanghui; Tindel, Samy
• 署名单位: CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; City University of New York (CUNY) System; Baruch College (CUNY); Purdue University System; Purdue University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2161
• 发表日期: 2025
• 页码: 1869-1912
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; weak; approximation; rates; ORDER

摘要

We prove that the Euler scheme for stochastic differential equations driven by fractional Brownian motions (fBm) with Hurst parameter H > 1/3 and its Malliavin derivatives are integrable uniformly in step size n. Then we use the integrability results to derive the weak convergence rate n1-4H+epsilon for the Euler scheme. The proof for integrability is based on an application of the argument of (Ann. Probab. 41 (2013) 3026-3050) to a quadratic functional of the fBm. The proof of weak convergence applies Malliavin calculus and some upper-bound estimates for weighted random sums.