The Annals of Applied Probability

Tail Events of some Nonhomogeneous Markov Chains

Wojciech Niemiro and Piotr Pokarowski

Full-text: Open access

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


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