Moshe Pollak

Let {*M*_{n}}_{n≥0} be a nonnegative time-homogeneous Markov process. The quasistationary distributions referred to in this note are of the form Q_{A}(*x*) = lim_{n→∞} P(M_{n} ≤ *x* | *M*_{0} ≤ *A*, *M*_{1} ≤ *A*, …, *M*_{n} ≤ *A*). Suppose that *M*_{0} has distribution Q_{A} and define *T*_{A}^{QA} = min{ n | *M*_{n} > *A*, *n* ≥ 1}, the first time when *M*_{n} exceeds *A*. We provide sufficient conditions for Q_{A}(*x*) to be nonincreasing in *A* (for fixed *x*) and for *T*_{A}^{QA} 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.