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August, 1977 Entrance Laws for Markov Chains
J. Theodore Cox
Ann. Probab. 5(4): 533-549 (August, 1977). DOI: 10.1214/aop/1176995759


Let $S$ be a countable set and let $Q$ be a stochastic matrix on $S \times S$. An entrance law for $Q$ is a collection $\mathbf{\mu} = \{\mu_n\}_{n\in\mathbb{Z}}$ of probability measures on $S$ such that $\mu_nQ = \mu_{n+1}$ for all $n\in\mathbb{Z}$. There is a natural correspondence between entrance laws and Markov chains $\xi_n$ with stationary transition probabilities $Q$ and time parameter set $\mathbb{Z}$. The set $\mathscr{L}(Q)$ of entrance laws is examined in the discrete and continuous time setting. Criteria are given which insure the existence of nontrivial entrance laws.


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J. Theodore Cox. "Entrance Laws for Markov Chains." Ann. Probab. 5 (4) 533 - 549, August, 1977.


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

zbMATH: 0369.60079
MathSciNet: MR455128
Digital Object Identifier: 10.1214/aop/1176995759

Primary: 60J10
Secondary: 60J50

Keywords: entrance laws , Markov chains , Martin boundary

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 4 • August, 1977
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