LIMIT DISTRIBUTIONS FOR THE DISCRETIZATION ERROR OF STOCHASTIC VOLTERRA EQUATIONS WITH FRACTIONAL KERNEL

• 成果类型: Article
• 署名作者: Fukasawa, Masaaki; Ugai, Takuto
• 署名单位: University of Osaka
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1941
• 发表日期: 2023
• 页码: 5071-5110
• 关键词: euler; schemes; THEOREM; sdes

摘要

Our study aims to specify the asymptotic error distribution in the dis-cretization of a stochastic Volterra equation with a fractional kernel. It is well known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence 1/root n, converges in law to the solution of a certain linear equation. Similar to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain linear Volterra equation with the same fractional ker-nel.