## The Annals of Probability

### Entrance Laws for Markov Chains

J. Theodore Cox

#### 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

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