Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Lévy processes
Abstract
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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- July 2012
- DOI:
- arXiv:
- arXiv:1202.2563
- Bibcode:
- 2012JMP....53g2701S
- Keywords:
-
- 05.40.-a;
- 05.45.-a;
- 02.50.Cw;
- 02.50.Ey;
- 02.60.Lj;
- 05.10.Gg;
- Fluctuation phenomena random processes noise and Brownian motion;
- Nonlinear dynamics and chaos;
- Probability theory;
- Stochastic processes;
- Ordinary and partial differential equations;
- boundary value problems;
- Stochastic analysis methods;
- Mathematics - Dynamical Systems;
- Mathematical Physics;
- Mathematics - Probability;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- 14 pages