Weak approximation for Gaussian processes from renewal processes
Probability
2025-11-24 v1
Abstract
In previous works, Bardina and Rovira (2023) constructed a family of processes that converge strongly towards Brownian motion, defined from renewal processes, are constructed. In this paper we prove that some of these processes can be utilized to build approximations of Gaussian processes such as fractional Brownian motion or multiple Stratonovich integrals and we provide sufficient conditions on renewal processes to ensure that the convergence holds. An illustrative example of such a Gaussian process is the fractional Brownian motion with any Hurst parameter.
Cite
@article{arxiv.2511.17280,
title = {Weak approximation for Gaussian processes from renewal processes},
author = {Xavier Bardina and Salim Boukfal and Marc Cano and Carles Rovira},
journal= {arXiv preprint arXiv:2511.17280},
year = {2025}
}
Comments
11 pages