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

Moshe Pollak*, Alexander G. Tartakovsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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) = limnn→∞ P(Mn ≤ x | M0 ≥ A, M1 ≥ A, . . . , Mn ≥ A). Suppose that M0 has distribution QA, and define T QAA = 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 TQAA to be stochastically nondecreasing in A.

Original languageEnglish
Pages (from-to)589-595
Number of pages7
JournalJournal of Applied Probability
Volume48
Issue number2
DOIs
StatePublished - Jun 2011

Keywords

  • Changepoint problem
  • First exit time
  • Markov process
  • Quasistationary distribution
  • Stationary distribution

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