On the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution
Copyright policy )On the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution
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 Q A = 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 Q A to be stochastically nondecreasing in A.
- University of California System United States
- Hebrew University of Jerusalem Israel
- University of Southern California United States
first exit time, Changepoint problem, stationary distribution, Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.), 60J05, changepoint problem, Discrete-time Markov processes on general state spaces, 62L15, quasistationary distribution, 62L10, Markov process, 60J20
first exit time, Changepoint problem, stationary distribution, Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.), 60J05, changepoint problem, Discrete-time Markov processes on general state spaces, 62L15, quasistationary distribution, 62L10, Markov process, 60J20
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