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

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

2010-06-04

arxiv.org/abs/1006.0965v1

Mathematics

Probability

6 pages

Scientific paper

Let {M_n}_{n\ge 0}$ be a nonnegative Markov process with stationary transition probabilities. The quasistationary distributions referred to in this note are of the form Q_A(x) = lim_{n\to\infty} P(M_n \le x | M_0 \le A, M_1 \le A, ..., M_n \le A) . Suppose that $M_0$ has distribution $\Qb_A$ and define T_A^{Q_A} = \min\{n | M_n > A, n\ge 1\}, the first time when M_n exceeds A. We provide sufficient conditions for E T_A^{Q_A}$ to be an increasing function of A.

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