Probabilistic models of vortex filaments

Franco Flandoli; Ida Minelli

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 4, page 713-731
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Flandoli, Franco, and Minelli, Ida. "Probabilistic models of vortex filaments." Czechoslovak Mathematical Journal 51.4 (2001): 713-731. <http://eudml.org/doc/30667>.

@article{Flandoli2001,
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.},
author = {Flandoli, Franco, Minelli, Ida},
journal = {Czechoslovak Mathematical Journal},
keywords = {stochastic integration; fractional Brownian motion; $p$-variation; vortex filaments; statistical fluid mechanics; stochastic integration; fractional Brownian motion; -variation; vortex filaments; statistical fluid mechanics},
language = {eng},
number = {4},
pages = {713-731},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Probabilistic models of vortex filaments},
url = {http://eudml.org/doc/30667},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Flandoli, Franco
AU - Minelli, Ida
TI - Probabilistic models of vortex filaments
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 713
EP - 731
AB - 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.
LA - eng
KW - stochastic integration; fractional Brownian motion; $p$-variation; vortex filaments; statistical fluid mechanics; stochastic integration; fractional Brownian motion; -variation; vortex filaments; statistical fluid mechanics
UR - http://eudml.org/doc/30667
ER -

References

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