Deviation inequalities for Banach space valued martingales differences sequences and random field

TL;DR

This paper develops deviation inequalities for the maxima of partial sums of Banach space-valued martingale differences and stationary orthomartingale random fields, aiding in understanding their convergence properties.

Contribution

It introduces new deviation inequalities for Banach space-valued martingale differences and orthomartingale random fields, extending existing probabilistic bounds.

Findings

Deviation inequalities for maxima of partial sums

Complete convergence results for normalized maxima

Applicability to Banach space-valued martingales

Abstract

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of normalized maxima of partial sums.