Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes

摘要

The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian Lévy processes, however, it is difficult to obtain explicit forms of Fokker-Planck equations, because the adjoint operators of the associated infinitesimal generators usually do not have exact formulation. In the present paper, Fokker-Planck equations are derived for nonlinear stochastic differential equations with non-Gaussian Lévy processes. A few examples are presented to illustrate the method.