1202.2563 (Xu Sun et al.)

Fokker-Planck equations for nonlinear dynamical systems driven by
non-Gaussian Levy processes    [PDF]

Xu Sun, Jinqiao Duan

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 L\'evy 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 in terms of infinite
series for nonlinear stochastic differential equations with non-Gaussian L\'evy
processes. A few examples are presented to illustrate the method.

View original: http://arxiv.org/abs/1202.2563