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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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