Journal of Applied Probability

On the first exit time of a nonnegative Markov process started at a quasistationary distribution

Moshe Pollak and Alexander G. Tartakovsky

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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.

Article information

J. Appl. Probab., Volume 48, Number 2 (2011), 589-595.

First available in Project Euclid: 21 June 2011

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Zentralblatt MATH identifier

Primary: 60J05: Discrete-time Markov processes on general state spaces 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
Secondary: 62L10: Sequential analysis 62L15: Optimal stopping [See also 60G40, 91A60]

Changepoint problem first exit time Markov process quasistationary distribution stationary distribution


Pollak, Moshe; Tartakovsky, Alexander G. On the first exit time of a nonnegative Markov process started at a quasistationary distribution. J. Appl. Probab. 48 (2011), no. 2, 589--595. doi:10.1239/jap/1308662648.

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