The Annals of Probability

Probabilistic models for vortex filaments based on fractional Brownian motion

David Nualart, Carles Rovira, and Samy Tindel

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Abstract

We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter $H>\frac{1}{2}.$ We show that the energy $\mathbb{H}$\vspace*{-1pt} has moments of any order under suitable conditions. When $H\in (\frac{1}{2},\frac{1}{3})$ we prove that the intersection energy $\mathbb{H}_{xy}$ can be decomposed into four terms, one of them being a weighted self-intersection local time of the fractional Brownian motion in $\mathbb{R}^{3}$.

Article information

Source
Ann. Probab., Volume 31, Number 4 (2003), 1862-1899.

Dates
First available in Project Euclid: 12 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1068646369

Digital Object Identifier
doi:10.1214/aop/1068646369

Mathematical Reviews number (MathSciNet)
MR2016603

Zentralblatt MATH identifier
1047.76013

Subjects
Primary: 76M35: Stochastic analysis 60H05: Stochastic integrals

Keywords
Filaments energy fractional Brownian motion

Citation

Nualart, David; Rovira, Carles; Tindel, Samy. Probabilistic models for vortex filaments based on fractional Brownian motion. Ann. Probab. 31 (2003), no. 4, 1862--1899. doi:10.1214/aop/1068646369. https://projecteuclid.org/euclid.aop/1068646369


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