Moment inequalities for sums of weakly dependent random fields

Description

We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangulargrid of dimension $d$ of a random field satisfying a weak dependency assumption of projective type:the difference between the expectation of an element of the random field and its conditional expectationgiven the rest of the field at a distance more than $\delta$ is bounded, in $L^p$distance, by a known decreasing function of $\delta$. The analysis is based on the combination of a multi-scale approximation of random sums by martingale difference sequences, andof a careful decomposition of the domain. The obtained results extend previously known bounds under comparable hypotheses, and do not use the assumption of commuting filtrations.

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