Exact convergence rates to derivatives of local time for some self-similar Gaussian processes

2024/07/07 by Minhao Hong, Hong, Minhao · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2407.05514

openalex publication_date 2024/07/07 · openalex created_date 2024/07/10 · openalex updated_date 2026/07/28

Abstract

In this article, for some d-dimensional Gaussian processes X=\X_t=(X¹_t,⋯,X^d_t):t≥0\, whose components are i.i.d. 1-dimensional self-similar Gaussian process with Hurst index H∈(0,1), we consider the asymptotic behavior of approximation of its \boldsymbolk-th derivatives of local time under certain mild conditions, where \boldsymbolk=(k₁,⋯,k_d) and k_ℓ's are non-negative real numbers. We will give a derivative version of the limit theorems for functional of Gaussian processes and use this result to get the asymptotic behaviors.

Cited by

• On the exponential integrability of the derivative of intersection and self-intersection local time for fractional Brownian motion and a limit theorem related to the self-intersection local time for fractional Brownian motion

Related

• Derivatives of local times for some Gaussian fields
• Limit theorems for additive functionals of some self-similar Gaussian processes
• On the passage times of self-similar Gaussian processes on curved boundaries
• Derivatives of local times for some Gaussian fields II
• Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes