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arXiv · 2508.07665

Regularization Effects of Time Integration on Gaussian Process Functionals

Takafumi Amaba·Marie Kratz
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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.

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Takafumi Amaba, Marie Kratz. 2025-08-11. Regularization Effects of Time Integration on Gaussian Process Functionals. https://arxiv.org/abs/2508.07665

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