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(Mn ≤ x | M0 ≤ A, M1 ≤ A, ..., Mn ≤ A). 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.
Citation
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
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