Probabilistic models for vortex filaments based on fractional Brownian motion

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.