Math. Model. Nat. Phenom.
Volume 13, Number 1, 2018
Theory and applications of fractional differentiation
|Number of page(s)||22|
|Published online||06 April 2018|
Fractional compound Poisson processes with multiple internal states
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University,
730000, P.R. China
* Corresponding author: email@example.com
Accepted: 24 September 2017
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. For the further application of the newly built models, we make very detailed discussions on the none-immediately-repeated stochastic process, e.g., the random walk of smart animals.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: Fractional compound Poisson processes / generalized Fokker-Planck equation / generalized Feynman-Kac equation / first passage time / non-repeat random walk
© EDP Sciences, 2018
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