## Journal of Applied Probability

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 21 June 2011

https://projecteuclid.org/euclid.jap/1308662648

Digital Object Identifier
doi:10.1239/jap/1308662648

Mathematical Reviews number (MathSciNet)
MR2840320

Zentralblatt MATH identifier
1218.60061

#### Citation

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. https://projecteuclid.org/euclid.jap/1308662648

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