Nonlinear stochastic equations with multiplicative Lévy noise

Details Nonlinear stochastic equations with multiplicative Lévy noise Nonlinear stochastic equations with multiplicative Lévy noise

2010-02-18

arxiv.org/abs/1002.3483v2

Phys. Rev. E81, 051110 (2010)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 7 figures

Scientific paper

The Langevin equation with a multiplicative L\'evy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed. The solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the Stratonovich interpretation. The problem of escaping from a potential well is analysed numerically; predictions of different interpretations of the stochastic integral are compared.

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