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1 results

  • On the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution

  • Part of
  • Moshe Pollak, Alexander G. Tartakovsky
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 2 / June 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 589-595
    Print publication:
    June 2011
    • Article
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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(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.