F. Flandoli, Dipartimento di Matematica Applicata, Universita di Pisa, Via Bonanno 25B, 56126 Pisa, Italy, e-mail: flandoli@dma.unipi.it; I. Minelli, Dipartimento di Matematica Pura e Applicata, Universita di Padova, Via G. Belzoni 7, 35131 Padova, Italy, e-mail: minelli@mail.dm.unipi.it
Abstract: A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between $1/2$ and $1$ are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.
Keywords: stochastic integration, fractional Brownian motion, $p$-variation, vortex filaments, statistical fluid mechanics
Classification (MSC 2000): 60H05, 60H30, 76M35, 76F55
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