LIMIT THEOREMS FOR ADDITIVE FUNCTIONALS OF SOME SELF-SIMILAR GAUSSIAN PROCESSES

• 成果类型: Article
• 署名作者: Hong, Minhao; Liu, Heguang; Xu, Fangjun
• 署名单位: Shanghai Maritime University; East China Normal University; East China Normal University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2096
• 发表日期: 2024
• 页码: 5462-5497
• 关键词: local-times

摘要

Under certain mild conditions, limit theorems for additive functionals of some d-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions, subfractional Brownian motions and bi-fractional Brownian motions. To prove these results, we use the method of moments and an enhanced chaining argument. The Gaussian processes under consideration are required to satisfy certain strong local nondeterminism property. A tractable sufficient condition for the strong local nondeterminism property is given and it only relays on the covariance functions of the Gaussian processes. Moreover, we give a sufficient condition for the distribution function of a random vector to be determined by its moments.