## Probabilistic models for vortex filaments based on fractional Brownian motion.(English)Zbl 1047.76013

Summary: 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 $$\mathbb{H}$$ 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 $$\mathbb{R}^{3}$$.

### MSC:

 76B47 Vortex flows for incompressible inviscid fluids 76M35 Stochastic analysis applied to problems in fluid mechanics 60H05 Stochastic integrals
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### References:

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