scholarly journals Fractional compound Poisson processes with multiple internal states

2018 ◽  
Vol 13 (1) ◽  
pp. 10 ◽  
Author(s):  
Pengbo Xu ◽  
Weihua Deng

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.

2012 ◽  
Vol 22 (5) ◽  
pp. 1860-1879 ◽  
Author(s):  
Marat V. Burnashev ◽  
Aslan Tchamkerten

2014 ◽  
Vol 25 (09) ◽  
pp. 1450037 ◽  
Author(s):  
Feng Zhu ◽  
Meifeng Dai ◽  
Yujuan Dong ◽  
Jie Liu

This paper reports a weighted hierarchical network generated on the basis of self-similarity, in which each edge is assigned a different weight in the same scale. We studied two substantial properties of random walk: the first-passage time (FPT) between a hub node and a peripheral node and the FPT from a peripheral node to a local hub node over the network. Meanwhile, an analytical expression of the average sending time (AST) is deduced, which reflects the average value of FPT from a hub node to any other node. Our result shows that the AST from a hub node to any other node is related to the scale factor and the number of modules. We found that the AST grows sublinearly, linearly and superlinearly respectively with the network order, depending on the range of the scale factor. Our work may shed some light on revealing the diffusion process in hierarchical networks.


2000 ◽  
Vol 273 (5-6) ◽  
pp. 322-330 ◽  
Author(s):  
Govindan Rangarajan ◽  
Mingzhou Ding

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