Open Access
February, 1977 Last Exit Times from the Boundary of a Continuous Time Markov Chain
Michael W. Chamberlain
Ann. Probab. 5(1): 152-156 (February, 1977). DOI: 10.1214/aop/1176995901


Probabilities of events involving the jump of a Markov chain to the state space immediately after the last exit before a given time from a boundary atom are determined, for the most part, by the initial time value of the canonical entrance law corresponding to that atom. Three of these probabilities are calculated in terms of canonical quantities in order to attach a probabilistic meaning to an entrance law decomposition of Reuter's and to improve an analytical condition of Chung's for when the Kolmogorov forward equations are satisfied by the chain's transition matrix.


Download Citation

Michael W. Chamberlain. "Last Exit Times from the Boundary of a Continuous Time Markov Chain." Ann. Probab. 5 (1) 152 - 156, February, 1977.


Published: February, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0363.60051
MathSciNet: MR431396
Digital Object Identifier: 10.1214/aop/1176995901

Primary: 60J10
Secondary: 60G17 , 60J25 , 60J35 , 60J50

Keywords: Chung's boundary theory , continuous time Markov chain , entrance laws , Kolmogorov forward equations , last exit times from boundary atoms , Reuter decomposition

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • February, 1977
Back to Top