Fokker-Planck Equations For Two Dimensions Nonlinear Dynamical Systems Driven By Non-Gaussian Levy Processes

With nonlinear programming is widely used in the practical life, the traditional planning method is difficult to solve nonlinear programming problems which have random disturbances, and in the actual work the planning problems trend to be complex dynamic system. So as to dealing with this kind of problems with random terms, stochastic differential equations play important roles in solving this issue. In order to have a good view of spread and propagation of random disturbances, this paper focuses on the Fokker-Planck equations which describe the density function of stochastic differential equations. Since many scholars have taken in-depth research, this paper will study the Fokker-Planck equations of Marcus integral stochastic differential equations in two-dimensions which has less research.Firstly the paper gives a detail introduction of the basic knowledge which involves the definition of Levy process, the Fokker-Planck equation's derivation process of Ito integral stochastic differential equations and Marcus integral stochastic differential equations. Then based on these theorems, the paper derives the Fokker-Planck equation of Marcus integral stochastic differential equations in second-order state by variable substitution, Ito formula, integration by parts, Fubini theorem and etc. Finally by use of the conclusions above, the paper gives the Fokker-Planck equation of Marcus integral stochastic differential equations in two-dimensions state.The paper respectively derives the Fokker-Planck equations of Marcus integral stochastic differential equations in second-order state and in two-dimensions state. Not only do these conclusions help research the spread and propagation of stochastic terms in second-order state and in two-dimensions state, but also promote the further derivation of Marcus integral stochastic differential equations in high-order state or in high-dimensions state.