On the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution
Moshe Pollak1, Alexander G. Tartakovsky2
1Statistics, The Hebrew University of Jerusalem, Jerusalem, Israel; 2Mathematics, The University of Southern California, Los Angeles, CA, United States

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.

Keywords: Quasistationary distribution; First exit time; Markov process; Changepoint problems

Biography: Moshe Pollak is Marcy Bogen Professor of Statistics at the Hebrew University of Jerusalem. His main line of research is in sequential statistical process control.