A family of log-correlated Gaussian processes
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915517928833024 |
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| author | Wang, Yizao |
| author_facet | Wang, Yizao |
| contents | A family of log-correlated Gaussian processes indexed by metric spaces is introduced, when the metric is conditionally negative definite. These processes arise as the limit of bi-fractional Brownian motions indexed by $(H,K)$ scaled by $K^{-1/2}$ as $K\downarrow 0$ with $H\in(0,1/2]$ fixed. When the metric is in addition a measure definite kernel, stochastic-integral representations of the generalized processes when evaluated at a test function are provided. The introduced processes are also shown to be the scaling limits of certain aggregated models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A family of log-correlated Gaussian processes Wang, Yizao Probability A family of log-correlated Gaussian processes indexed by metric spaces is introduced, when the metric is conditionally negative definite. These processes arise as the limit of bi-fractional Brownian motions indexed by $(H,K)$ scaled by $K^{-1/2}$ as $K\downarrow 0$ with $H\in(0,1/2]$ fixed. When the metric is in addition a measure definite kernel, stochastic-integral representations of the generalized processes when evaluated at a test function are provided. The introduced processes are also shown to be the scaling limits of certain aggregated models. |
| title | A family of log-correlated Gaussian processes |
| topic | Probability |
| url | https://arxiv.org/abs/2412.06615 |