Fokker-Planck Type Equation Of A Class Of Compound Process

Diffusion process in complex system are widely applied in physics, chemistry, finance and other science fields. The problem of diffusion process and Fokker-Planck equation is s-tudied in recent years, Magdziarz proved that in the external potential, the probability density function of compound process X(Sα(t)) is the solution to the classic fractional Fokker-Planck equation. In this paper, we consider the Fokker-Planck type equation which is equivalent to a class of compound stochastic process related with coupled continuous time random walk. Firstly we introduce cluster continuous time random walk model which infers compound process Y-(t)= X(U(Sα(t))) and Y+(t)= X(O(Sα(t))). And then we apply Fourier Laplace transform method to deduce the Fokker-Planck type equation which is equivalent to random process Y-(t) and Y+(t). Moreover, with the special condition, the result of this paper is degraded into the related conclusion in [23].