Sojourn times

Lajos Takács

International Journal of Stochastic Analysis, 1996, vol. 9, 1-12

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:465401

DOI: 10.1155/S1048953396000366

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