Fractional compound Poisson processes with multiple internal states

Abstract

For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and functional distributions of the trajectories of particles; in particular, the equations governing the functional distribution of internal states are also obtained. The dynamics of the stochastic processes are analyzed and the applications, calculating the distribution of the first passage time and the distribution of the fraction of the occupation time, of the equations are given.

5 pages, 2 figures

References in corpus (5)

• Anomalous Diffusion of Inertial, Weakly Damped Particles
• On distributions of functionals of anomalous diffusion paths
• Amnestically induced persistence in random walks
• First passage time statistics for two-channel diffusion
• Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times

Cited by in corpus (7)

• Nonlocal Diffusion Operators for Normal and Anomalous Dynamics
• Feynman-Kac equation revisited
• Fast algorithms for convolution quadrature of Riemann-Liouville fractional derivative
• Aging two-state process with Lévy walk and Brownian motion
• Levy walk with multiple internal states
• Numerical algorithm for the space-time fractional Fokker-Planck system with two internal states
• Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal states