WEAK WELL-POSEDNESS OF STOCHASTIC VOLTERRA EQUATIONS WITH COMPLETELY MONOTONE KERNELS AND NONDEGENERATE NOISE

• 成果类型: Article
• 署名作者: Hamaguchi, Yushi
• 署名单位: Kyoto University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/25-AAP2149
• 发表日期: 2025
• 页码: 1442-1488
• 关键词: harnack inequality; uniqueness; EXISTENCE; LIMITS; pdes

摘要

We establish weak existence and uniqueness in law for stochastic Volterra equations (SVEs for short) with completely monotone kernels and nondegenerate noise under mild regularity assumptions. In particular, our results reveal the regularization-by-noise effect for SVEs with singular kernels, allowing for multiplicative noise with H & ouml;lder diffusion coefficients. In order to prove our results, we reformulate the SVE into an equivalent stochastic evolution equation (SEE for short) defined on a Gelfand triplet of Hilbert spaces. We prove weak well-posedness of the SEE using stochastic control arguments, and then translate it into the original SVE.