Central Limit Theorem for truncated heavy tailed Banach valued random vectors

TL;DR

This paper investigates how truncating heavy-tailed Banach space-valued random vectors affects their convergence properties, specifically examining the applicability of the central limit theorem to such truncated vectors.

Contribution

It provides new insights into the behavior of truncated heavy-tailed vectors in Banach spaces concerning the central limit theorem, a topic not extensively explored before.

Findings

Truncated heavy-tailed vectors can still satisfy a form of the central limit theorem.

The extent of tail truncation influences the convergence behavior.

Conditions under which the CLT holds for truncated vectors are characterized.

Abstract

In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central limit theorem.