H\"older estimates and weak convergences of certain weighted sum processes
Probability
2025-10-09 v3
Abstract
We study weighted sum processes associated to elements in a Wiener chaos with fixed order. More precisely, we show H\"older estimates and a functional limit theorem for them. Main tools we use are the integration by parts formula in Malliavin calculus, the fourth moment theorem, and estimates in multidimensional Young integrals.
Cite
@article{arxiv.2408.05255,
title = {H\"older estimates and weak convergences of certain weighted sum processes},
author = {Shigeki Aida and Nobuaki Naganuma},
journal= {arXiv preprint arXiv:2408.05255},
year = {2025}
}
Comments
This version is accepted for publication in Journal of Theoretical Probability. There are some overlap with arXiv:2302.03912