Journal of Applied Mathematics and Stochastic Analysis 
Volume 9 (1996), Issue 4, Pages 415-426
doi:10.1155/S1048953396000366

Sojourn times

Lajos Takács1,2

 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

Abstract

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.