Regularization Effects of Time Integration on Gaussian Process Functionals
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908484309614592 |
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| author | Amaba, Takafumi Kratz, Marie |
| author_facet | Amaba, Takafumi Kratz, Marie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07665 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization Effects of Time Integration on Gaussian Process Functionals Amaba, Takafumi Kratz, Marie Probability Statistics Theory 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. |
| title | Regularization Effects of Time Integration on Gaussian Process Functionals |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2508.07665 |