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A Family of Log-Correlated Gaussian Processes

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  • Yizao Wang

    (University of Cincinnati)

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 $$K^{-1/2}$$ K - 1 / 2 as $$K\downarrow 0$$ K ↓ 0 with $$H\in (0,1/2]$$ H ∈ ( 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.

Suggested Citation

  • Yizao Wang, 2025. "A Family of Log-Correlated Gaussian Processes," Journal of Theoretical Probability, Springer, vol. 38(4), pages 1-34, December.
    • Handle: RePEc:spr:jotpro:v:38:y:2025:i:4:d:10.1007_s10959-025-01449-2
    DOI: 10.1007/s10959-025-01449-2
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