## The Annals of Probability

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

### Entrance Laws for Markov Chains

#### 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