Probabilistic models for vortex filaments based on fractional Brownian motion
Nualart, David ; Rovira, Carles ; Tindel, Samy
Ann. Probab., Tome 31 (2003) no. 1, p. 1862-1899 / Harvested from Project Euclid
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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 $\mathbb{R}^{3}$.
Publié le : 2003-10-14
Classification:  Filaments,  energy,  fractional Brownian motion,  76M35,  60H05 
@article{1068646369,
     author = {Nualart, David and Rovira, Carles and Tindel, Samy},
     title = {Probabilistic models for vortex filaments based on fractional Brownian motion},
     journal = {Ann. Probab.},
     volume = {31},
     number = {1},
     year = {2003},
     pages = { 1862-1899},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1068646369}
}

Nualart, David; Rovira, Carles; Tindel, Samy. Probabilistic models for vortex filaments based on fractional Brownian motion. Ann. Probab., Tome 31 (2003) no. 1, pp.  1862-1899. http://gdmltest.u-ga.fr/item/1068646369/