Probabilistic models for vortex filaments based on fractional Brownian motion

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