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Journal of Applied Mathematics and Stochastic Analysis
Volume 9, Issue 4, Pages 415-426
http://dx.doi.org/10.1155/S1048953396000366

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1Case Western Reserve University, Department of Mathematics, Cleveland 44106, OH, USA
22410 Newbury Drive, Cleveland Heights 44118, Ohio, USA

Received 1 April 1996; Revised 1 July 1996

Copyright © 1996 Hindawi Publishing Corporation. 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.

Abstract

Let {ζ(u),u0} be a stochastic process with state space AB where A and B are disjoint sets. Denote by β(t) the total time spent in state B in the interval (0,t). This paper deals with the problem of finding the distribution of β(t) and the asymptotic distribution of β(t) as t for various types of stochastic processes. The main result is a combinatorial theorem which makes it possible to find in an elementary way, the distribution of β(t) for homogeneous stochastic processes with independent increments.

This article is dedicated to the memory of Roland L. Dobrushin.