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June 2011 On the first exit time of a nonnegative Markov process started at a quasistationary distribution
Moshe Pollak, Alexander G. Tartakovsky
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J. Appl. Probab. 48(2): 589-595 (June 2011). DOI: 10.1239/jap/1308662648

Abstract

Let {Mn}n≥0 be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form QA(x) = limn→∞P(Mnx | M0A, M1A, ..., MnA). Suppose that M0 has distribution QA, and define TAQA = min{n | Mn > A, n ≥ 1}, the first time when Mn exceeds A. We provide sufficient conditions for QA(x) to be nonincreasing in A (for fixed x) and for TAQA to be stochastically nondecreasing in A.

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Moshe Pollak. Alexander G. Tartakovsky. "On the first exit time of a nonnegative Markov process started at a quasistationary distribution." J. Appl. Probab. 48 (2) 589 - 595, June 2011. https://doi.org/10.1239/jap/1308662648

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1218.60061
MathSciNet: MR2840320
Digital Object Identifier: 10.1239/jap/1308662648

Subjects:
Primary: 60J05, 60J20
Secondary: 62L10, 62L15

Rights: Copyright © 2011 Applied Probability Trust

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Vol.48 • No. 2 • June 2011
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