Associated Sequences and Demimartingales: An Overview

Abstract: We present an overview of the concepts of associated sequences of random variables and demimartingales and give a review of their probabilistic properties such as laws of large numbers, central limit theorems and up crossing inequalities. It is known that a martingale with respect to the natural sequence of sigma algebras forms a demimartingale but not all demimatingales are generated in this form. It is all known that partial sums of zero mean associated random variables forms a demimartingale but not all demimartingales are generated from such zero mean associated sequences of random variables.

probabilitystatistics theorydata analysis, statistics and probability

Audience: researchers in the topic

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Asymptotic Methods in Statistics

Series comments: One can find video files and slides of talks at the seminar on Asymptotic Methods in Statistics here: www.youtube.com/@SeminarforAsymptoticMethods

A link to a slide is below the description of the video, namely shorturl.at/jUAhL and shorturl.at/6wjUA shorturl.at/rdpqs

Alas the links do not work in one click: you should emphasize them with a mouse and select, e.g., "Go to shorturl.at/rdpqs".

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