A Family of Log-Correlated Gaussian Processes

Yizao Wang ()
Additional contact information
Yizao Wang: University of Cincinnati

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-34

Abstract: 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.

Keywords: Log-correlated Gaussian process; Fractional Brownian motion; Bi-fractional Brownian motion; 60G20; 60G22; 60F05 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-025-01449-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:38:y:2025:i:4:d:10.1007_s10959-025-01449-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-025-01449-2

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().