Multiplicative Lévy processes: Itô versus Stratonovich interpretation

Details Multiplicative Lévy processes: Itô versus Stratonovich interpretation Multiplicative Lévy processes: Itô versus Stratonovich interpretation

2009-06-08

arxiv.org/abs/0906.1395v2

Phys. Rev. E80, (2009) 051113

Physics

Condensed Matter

Statistical Mechanics

11 pages, 6 figures

Scientific paper

Langevin equation with a multiplicative stochastic force is considered. That force is uncorrelated, it has the L\'evy distribution and the power-law intensity. The Fokker-Planck equations, which correspond both to the It\^o and Stratonovich interpretation of the stochastic integral, are presented. They are solved for the case without drift and for the harmonic oscillator potential. The variance is evaluated; it is always infinite for the It\^o case whereas for the Stratonovich one it can be finite and rise with time slower that linearly, which indicates subdiffusion. Analytical results are compared with numerical simulations.

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