QUANTIFYING A CONVERGENCE THEOREM OF GYoNGY AND KRYLOV

• 成果类型: Article
• 署名作者: Dareiotis, Konstantinos; Gerencser, Mate; Le, Khoa
• 署名单位: University of Leeds; Technische Universitat Wien; Technical University of Berlin
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1867
• 发表日期: 2023
• 页码: 2291-2323
• 关键词: euler-maruyama scheme; multidimensional sdes; stochastic-equations; occupation time; approximation; drift; EXISTENCE

摘要

We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order alpha e (0, 1) lead to rate (1 + alpha )/2.