## The Annals of Applied Probability

- Ann. Appl. Probab.
- Volume 5, Number 1 (1995), 261-293.

### Tail Events of some Nonhomogeneous Markov Chains

Wojciech Niemiro and Piotr Pokarowski

#### Abstract

We consider finite state nonhomogeneous Markov chains with one-step transition probabilities roughly proportional to powers of a small parameter, converging to zero. We examine asymptotic properties of trajectories. The analysis is based on the so-called orders of recurrence. Transient states, recurrent classes and periodic subclasses can be identified in terms of the matrix of powers. This leads to a complete description of the tail sigma field. Our theorems generalize the classical results for homogeneous chains and can also be applied to chains generated by stochastic algorithms of the "simulated annealing" type.

#### Article information

**Source**

Ann. Appl. Probab., Volume 5, Number 1 (1995), 261-293.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoap/1177004840

**Digital Object Identifier**

doi:10.1214/aoap/1177004840

**Mathematical Reviews number (MathSciNet)**

MR1325053

**Zentralblatt MATH identifier**

0826.60055

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Secondary: 90C15: Stochastic programming

**Keywords**

Nonhomogeneous Markov chain tail sigma field orders of recurrence simulated annealing

#### Citation

Niemiro, Wojciech; Pokarowski, Piotr. Tail Events of some Nonhomogeneous Markov Chains. Ann. Appl. Probab. 5 (1995), no. 1, 261--293. doi:10.1214/aoap/1177004840. https://projecteuclid.org/euclid.aoap/1177004840