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

2010/06/04 by Moshe Pollak, Alexander G. Tartakovsky, Pollak, Moshe +1 · 1 citation
Business, Management and Accounting · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60J20 #62L15 #Advanced Queuing Theory Analysis #Advanced Statistical Process Monitoring #FOS: Mathematics #Primary 60J05 #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #secondary 62L10

paper · pdf · doi:10.48550/arxiv.1006.0965

openalex publication_date 2010/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M_{nn\≥ 0} be a nonnegative Markov process with stationary\ntransition probabilities. The quasistationary distributions referred to in this\nnote are of the form Q_A(x) = lim_n\→\∞ P(M_n \≤ x | M₀ \≤ A, M₁ \≤\nA, ..., M_n \≤ A) . Suppose that M₀ has distribution Qb_A and define\nT_A^Q_A = \min n | M_n > A, n\≥ 1 , the first time when M_n exceeds A. We\nprovide sufficient conditions for E T_A^Q_A to be an increasing function of\nA.\n

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