The Annals of Probability

Entrance Laws for Markov Chains

J. Theodore Cox

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Abstract

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.

Article information

Source
Ann. Probab., Volume 5, Number 4 (1977), 533-549.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995759

Digital Object Identifier
doi:10.1214/aop/1176995759

Mathematical Reviews number (MathSciNet)
MR455128

Zentralblatt MATH identifier
0369.60079

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J50: Boundary theory

Keywords
Entrance laws Markov chains Martin boundary

Citation

Cox, J. Theodore. Entrance Laws for Markov Chains. Ann. Probab. 5 (1977), no. 4, 533--549. doi:10.1214/aop/1176995759. https://projecteuclid.org/euclid.aop/1176995759


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