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October 2003 Probabilistic models for vortex filaments based on fractional Brownian motion
David Nualart, Carles Rovira, Samy Tindel
Ann. Probab. 31(4): 1862-1899 (October 2003). DOI: 10.1214/aop/1068646369

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 $\mathbb{R}^{3}$.

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David Nualart. Carles Rovira. Samy Tindel. "Probabilistic models for vortex filaments based on fractional Brownian motion." Ann. Probab. 31 (4) 1862 - 1899, October 2003. https://doi.org/10.1214/aop/1068646369

Information

Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1047.76013
MathSciNet: MR2016603
Digital Object Identifier: 10.1214/aop/1068646369

Subjects:
Primary: 60H05, 76M35

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • October 2003
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