Sojourn times

Takács, Lajos

doi:https://doi.org/10.1155/S1048953396000366

International Journal of Stochastic Analysis

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

Lajos Takács, "Sojourn times", International Journal of Stochastic Analysis, vol. 9, Article ID 465401, 12 pages, 1996. https://doi.org/10.1155/S1048953396000366

Sojourn times

Lajos Takács^1,2

¹Case Western Reserve University, Department of Mathematics, USA

²2410 Newbury Drive, USA

Received01 Apr 1996

Revised01 Jul 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.

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.

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