## The Annals of Probability

### Markov Chains in Random Environments: The Case of Markovian Environments

Robert Cogburn

#### Abstract

A formulation of a Markov chain in a random environment is given, generalizing special cases such as branching processes, queues, birth and death chains and random walks in random environments. It is assumed that the environmental process is Markovian, each environment corresponding to a particular law of evolution on a countable state space $\mathscr{X}$. It is then shown that there is a natural three way classification of states of $\mathscr{X}$. One of the three types of states is irregular in nature, and conditions are found under which no such states exist.

#### Article information

Source
Ann. Probab. Volume 8, Number 5 (1980), 908-916.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994620

Digital Object Identifier
doi:10.1214/aop/1176994620

Mathematical Reviews number (MathSciNet)
MR586775

Zentralblatt MATH identifier
0444.60053

JSTOR

#### Citation

Cogburn, Robert. Markov Chains in Random Environments: The Case of Markovian Environments. Ann. Probab. 8 (1980), no. 5, 908--916. doi:10.1214/aop/1176994620. https://projecteuclid.org/euclid.aop/1176994620