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Monotonicity of Positive Dependence with Time for Stationary Reversible Markov Chains

Published online by Cambridge University Press:  27 July 2009

Taizhong Hu  and
Harry Joe
Taizhong Hu
Affiliation:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
Harry Joe
Affiliation:
Department of Statistics, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2
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Abstract

Let (X1, X2) and (Y1, Y2) be bivariate random vectors with a common marginal distribution (X1, X2) is said to be more positively dependent than (Y1, Y2) if E[h(X1)h(X2)] ≥ E[h(Y1)h(Y2)] for all functions h for which the expectations exist. The purpose of this paper is to study the monotonicity of positive dependence with time for a stationary reversible Markov chain [X1]; that is, (Xs, Xl+s) is less positively dependent as t increases. Both discrete and continuous time and both a denumerable set and a subset of the real line for the state space are considered. Some examples are given to show that the assertions established for reversible Markov chains are not true for nonreversible chains.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 227 - 237
Copyright
Copyright © Cambridge University Press 1995

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