Nonlinear stochastic equations with multiplicative Lévy noise
arXiv:1002.3483 · doi:10.1103/PhysRevE.81.051110
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