Work

Limit theorems for additive functionals of some self-similar Gaussian processes

Year: 2024

Type: article

Abstract: 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.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2096

Authors: Minhao Hong, Heguang Liu, Fangjun Xu

Institutions: Shanghai Maritime University, East China Normal University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: 高斯过程非线性泛函极限理论的若干问题研究