An Alternate Proof of a Correlation Inequality of Harris

J. Theodore Cox

doi:10.1214/aop/1176993391

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Home > Journals > Ann. Probab. > Volume 12 > Issue 1 > Article

February, 1984 An Alternate Proof of a Correlation Inequality of Harris

J. Theodore Cox

Ann. Probab. 12(1): 272-273 (February, 1984). DOI: 10.1214/aop/1176993391

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Abstract

A theorem of Harris states that a monotone Markov process on a finite partially ordered set has positive correlations at time $t$ (assuming positive correlations at time 0) if and only if each jump of the process is either up or down. A new proof of the sufficiency of the jump condition is presented.

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J. Theodore Cox. "An Alternate Proof of a Correlation Inequality of Harris." Ann. Probab. 12 (1) 272 - 273, February, 1984. https://doi.org/10.1214/aop/1176993391