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On the theory of Markov set-chains

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

D. J. Hartfiel  and
E. Seneta
D. J. Hartfiel*
Affiliation:
Texas A&M University
E. Seneta*
Affiliation:
University of Sydney
*
* Postal address: Mathematics Department, Texas A&M University, College Station, TX 77843, USA.
** Postal address: School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia.
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Abstract

In the theory of homogeneous Markov chains, states are classified according to their connectivity to other states and this classification leads to a classification of the Markov chains themselves. In this paper we classify Markov set-chains analogously, particularly into ergodic, regular, and absorbing Markov set-chains. A weak law of large numbers is developed for regular Markov set-chains. Examples are used to illustrate analysis of behavior of Markov set-chains.

Keywords

WEAK LAW OF LARGE NUMBERSCOEFFICIENT OF ERGODICITYASYMPTOTICS OF MARKOV SET-CHAINS

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 26 , Issue 4 , December 1994 , pp. 947 - 964
Copyright
Copyright © Applied Probability Trust 1994 

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