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Probabilistic models for vortex filaments based on fractional Brownian motion

Nualart, David
; 
Rovira, Carles
; 
Tindel, Samy
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Abstract
We consider a vortex structure based on a three-dimensional fractional Brownian motion with Hurst parameter H>12. We show that the energy H\vspace*{-1pt} has moments of any order under suitable conditions. When H∈(12,13) we prove that the intersection energy Hxy can be decomposed into four terms, one of them being a weighted self-intersection local time of the fractional Brownian motion in R3.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1068646369.
Date
2003-11-01
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Volume Title
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Institute of Mathematical Statistics (IMS)
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Mathematics Scholarly Works
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NualartD_AP_31(4)1862.pdf
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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. http://dx.doi.org/10.1214/aop/1068646369.
URI
https://hdl.handle.net/1808/17049
DOI
10.1214/aop/1068646369
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