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Advances in Mathematical Physics
Volume 2010, Article ID 504267, 12 pages
Research Article

On the Exact Solution of a Generalized Polya Process

Department of Risk Engineering, Faculty of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan

Received 1 August 2010; Accepted 10 October 2010

Academic Editor: Pierluigi Contucci

Copyright © 2010 Hidetoshi Konno. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


There are two types of master equations in describing nonequilibrium phenomena with memory effect: (i) the memory function type and (ii) the nonstationary type. A generalized Polya process is studied within the framework of a non-stationary type master equation approach. For a transition-rate with an arbitrary time-dependent relaxation function, the exact solution of a generalized Polya process is obtained. The characteristic features of temporal variation of the solution are displayed for some typical time-dependent relaxation functions reflecting memory in the systems.