Let {ζ(u),u≥0} be a stochastic process with state space A∪B 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
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.
PDF
