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February, 1984 Almost Sure Convergence of Multiparameter Martingales for Markov Random Fields
Hans Follmer
Ann. Probab. 12(1): 133-140 (February, 1984). DOI: 10.1214/aop/1176993378

Abstract

We prove that bounded multiparameter martingales converge almost surely if the underlying $\sigma$-fields are generated by a Markov random field which satisfies Dobrushin's uniqueness condition. An example shows that it is not enough to assume that the Markov field is uniquely determined by its conditional probabilities.

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Hans Follmer. "Almost Sure Convergence of Multiparameter Martingales for Markov Random Fields." Ann. Probab. 12 (1) 133 - 140, February, 1984. https://doi.org/10.1214/aop/1176993378

Information

Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0538.60043
MathSciNet: MR723734
Digital Object Identifier: 10.1214/aop/1176993378

Subjects:
Primary: 60G42
Secondary: 60K35 , 82A67

Keywords: Dobrushin's uniqueness condition , Markov random fields , Multiparameter martingales

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February, 1984
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