English

Regularization Effects of Time Integration on Gaussian Process Functionals

Probability 2025-08-12 v1 Statistics Theory Statistics Theory

Abstract

In this paper, we investigate the regularization effects, in the sense of Malliavin calculus, on functionals of Gaussian processes induced by time integration, focusing on their covariance functions. We study several examples of important covariance functions classes to verify whether they satisfy the sufficient conditions proposed for regularization. Additionally, we derive a weak implication for the smoothness of level-crossing functionals.

Cite

@article{arxiv.2508.07665,
  title  = {Regularization Effects of Time Integration on Gaussian Process Functionals},
  author = {Takafumi Amaba and Marie Kratz},
  journal= {arXiv preprint arXiv:2508.07665},
  year   = {2025}
}

Comments

31 pages

R2 v1 2026-07-01T04:43:42.741Z