Moment inequalities for sums of weakly dependent random fields - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2023

Moment inequalities for sums of weakly dependent random fields

Abstract

We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangular grid 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 expectation given 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, and of 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.
Fichier principal
Vignette du fichier
REVISION_bernoulli_dependentspatialsprocesses.pdf (270.73 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04150509 , version 1 (04-07-2023)

Identifiers

Cite

Gilles Blanchard, Alexandra Carpentier, Oleksandr Zadorozhnyi. Moment inequalities for sums of weakly dependent random fields. 2023. ⟨hal-04150509⟩
16 View
33 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More