HELLINGER AND TOTAL VARIATION DISTANCE IN APPROXIMATING LeVY DRIVEN SDES

• 成果类型: Article
• 署名作者: Clement, Emmanuelle
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1863
• 发表日期: 2023
• 页码: 2176-2209
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; euler approximation; CONVERGENCE; diffusion; EXISTENCE; scheme

摘要

In this paper, we get some convergence rates in total variation distance in approximating discretized paths of Levy driven stochastic differential equa-tions, assuming that the driving process is locally stable. The particular case of the Euler approximation is studied. Our results are based on sharp local estimates in Hellinger distance obtained using Malliavin calculus for jump processes.