A family of log-correlated Gaussian processes

Yizao Wang

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arXiv · 2412.06615

A family of log-correlated Gaussian processes

Yizao Wang

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Abstract

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.

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Yizao Wang. 2024-12-09. A family of log-correlated Gaussian processes. https://arxiv.org/abs/2412.06615

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