Nonlinear stochastic equations with multiplicative Lévy noise

Abstract

The Langevin equation with a multiplicative Lévy 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.

10 pages, 7 figures

References in corpus (3)

• Escape driven by $\alpha$-stable white noises
• Fractional Fokker-Planck equation for Lévy flights in nonhomogeneous environments
• Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media

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