On stable central limit theorems for multivariate discrete-time martingales

TL;DR

This paper develops a systematic approach to establish stable central limit theorems for multivariate martingale difference arrays and sequences, extending univariate conditions to higher dimensions.

Contribution

It introduces straightforward conditions for multivariate stable CLTs, generalizing existing univariate results to the multivariate setting.

Findings

Provides a unified framework for multivariate stable CLTs.

Extends univariate conditions to the multivariate case.

Facilitates analysis of high-dimensional martingale processes.

Abstract

We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.