Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 415-426
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 Lajos Takács. 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.
Let be a stochastic process with state space where and
are disjoint sets. Denote by the total time spent in state in the interval
. This paper deals with the problem of finding the distribution of and
the asymptotic distribution of as 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 for homogeneous stochastic processes with independent increments.
This article is dedicated to the memory of Roland L. Dobrushin.