Dependence ordering for Markov processes on partially ordered spaces
Hans Daduna and Ryszard Szekli
Source: J. Appl. Probab. Volume 43, Number 3 (2006), 793-814.
Abstract
We compare dependence in stochastically monotone Markov processes with partially ordered Polish state spaces using the concordance and supermodular orders. We show necessary and sufficient conditions for the concordance order to hold both in terms of the one-step transition probabilities for discrete-time processes and in terms of the corresponding infinitesimal generators for continuous-time processes. We give examples showing that a stochastic monotonicity assumption is not necessary for such orderings. We indicate relations between dependence orderings and, variously, the asymptotic variance-reduction effect in Monte Carlo Markov chains, Cheeger constants, and positive dependence for Markov processes.
Primary Subjects: 60J25, 60K25
Keywords: Concordance order; supermodular order; stochastic monotonicity; monotone Markov process; dependence order; Cheeger constant; association; MCMC
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1158784947
Digital Object Identifier: doi:10.1239/jap/1158784947
Mathematical Reviews number (MathSciNet):
MR2274801
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