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February, 1995 Tail Events of some Nonhomogeneous Markov Chains
Wojciech Niemiro, Piotr Pokarowski
Ann. Appl. Probab. 5(1): 261-293 (February, 1995). DOI: 10.1214/aoap/1177004840


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.


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Wojciech Niemiro. Piotr Pokarowski. "Tail Events of some Nonhomogeneous Markov Chains." Ann. Appl. Probab. 5 (1) 261 - 293, February, 1995.


Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0826.60055
MathSciNet: MR1325053
Digital Object Identifier: 10.1214/aoap/1177004840

Primary: 60J10
Secondary: 90C15

Keywords: nonhomogeneous Markov chain , orders of recurrence , simulated annealing , tail sigma field

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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