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June, 1974 Sojourn Time Problems
Lajos Takacs
Ann. Probab. 2(3): 420-431 (June, 1974). DOI: 10.1214/aop/1176996657

Abstract

It is supposed that in the time interval $(0, \infty)$ a stochastic process is alternately in states $A$ and $B$. Denote by $\alpha_1, \beta_1, \alpha_2, \beta_2, \cdots$ the lengths of the successive intervals spent in states $A$ and $B$ respectively. In this paper the distribution and the asymptotic distribution of the total time spent in state $A(B)$ in the interval $(0, t)$ are determined in the case where $(\alpha_1, \beta_1), (\alpha_2, \beta_2), \cdots$ are mutually independent and identically distributed vector variables.

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Lajos Takacs. "Sojourn Time Problems." Ann. Probab. 2 (3) 420 - 431, June, 1974. https://doi.org/10.1214/aop/1176996657

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0323.60054
MathSciNet: MR358974
Digital Object Identifier: 10.1214/aop/1176996657

Subjects:
Primary: 60G50
Secondary: 60F05

Keywords: exact distributions , examples , limiting distributions , sojourn times

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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