English

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.

Keywords

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