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June, 1977 A Correlation Inequality for Markov Processes in Partially Ordered State Spaces
T. E. Harris
Ann. Probab. 5(3): 451-454 (June, 1977). DOI: 10.1214/aop/1176995804

Abstract

Let $E$ be a finite partially ordered set and $M_p$ the set of probability measures in $E$ giving a positive correlation to each pair of increasing functions on $E$. Given a Markov process with state space $E$ whose transition operator (on functions) maps increasing functions into increasing functions, let $U_t$ be the transition operator on measures. In order that $U_tM_p \subset M_p$ for each $t \geqq 0$, it is necessary and sufficient that every jump of the sample paths is up or down.

Citation

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T. E. Harris. "A Correlation Inequality for Markov Processes in Partially Ordered State Spaces." Ann. Probab. 5 (3) 451 - 454, June, 1977. https://doi.org/10.1214/aop/1176995804

Information

Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0381.60072
MathSciNet: MR433650
Digital Object Identifier: 10.1214/aop/1176995804

Subjects:
Primary: 60B99
Secondary: 60K35

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 3 • June, 1977
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