From the Ehrenfest model to time-fractional stochastic processes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Abdel-Rehim, E. A.

关键词: Ehrenfest urn model;    Diffusion processes;    Central drift;    Difference schemes;    Time-fractional derivative;    Stochastic processes;    Reversible processes;   

DOI  :  10.1016/j.cam.2009.07.010

来源: Elsevier

【 摘 要 】

The Ehrenfest model is considered as a good example of a Markov chain. 1 prove in this paper that the time-fractional diffusion process with drift towards the origin, is a natural generalization of the modified Ehrenfest model. The corresponding equation of evolution is a linear partial pseudo-differential equation with fractional derivatives in time, the orders lying between 0 and 1.1 focus oil finding a precise explicit analytical Solution to this equation depending on the interval of the time. The stationary solution of this model is also analytically and numerically calculated. Then I prove that the difference between the discrete approximate Solution at time t(n). for all n >= 0, and the stationary solution obeys a power law with exponent between 0 and 1. The reversibility property is discussed for the Ehrenfest model and its fractional version with a new observation. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free