Fokker-Planck Equations For Stochastic Dynamical Systems Driven By Non-gaussian Levy Processes

The Fokker-Planck equation describes the evolution of the probability density and it has played an important role in the study of stochastic dynamical. Non-Gaussian Levy process is a common stochastic process. The study of Fokker-Planck equations for stochastic dynamical systems driven by non-Gaussian Levy processes is of great significance.The main objective of this thesis is to study Fokker-Planck equations for stochastic dynamical systems driven by non-Gaussian Levy processes.This paper consists of five parts. The first part reviews some existed results about Fokker-Planck equations. The second part is prior knowledge, including some definitions and theorems which are necessary to derive the Fokker-Planck equations for stochastic dynamical systems driven by non-Gaussian Levy processes. The third part introduces the definitions of backward Kolmogorov equation and the forward Kolmogorov equation. The fourth part is the Fokker-Planck equation for Levy processes. In this part, we first give some preliminary concepts for Levy processes, then we derive the Fokker-Planck equations for stochastic differential equations in Ito form and Marcus form, respectively.The conclusion of this thesis is that we can get the Fokker-Planck equations for stochastic dynamical systems driven by non-Gaussian Levy processes. The theoretical analysis is verified by numerical examples.