International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1996 / Article

Open Access

Volume 9 |Article ID 465401 | 12 pages | https://doi.org/10.1155/S1048953396000366

Sojourn times

Received01 Apr 1996
Revised01 Jul 1996

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.

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.


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