On nonlinear weak law of large numbers

TL;DR

This paper introduces a new nonlinear weak law of large numbers that does not require the existence of first moments and relaxes independence assumptions, expanding the theoretical understanding of convergence in probability.

Contribution

It proposes a novel version of the nonlinear weak law of large numbers without assuming first moments and with relaxed independence conditions.

Findings

Established a new form of nonlinear weak law of large numbers

Removed the requirement for the existence of first moments

Relaxed the independence assumption in the law

Abstract

A new version of a weak nonlinear law of large numbers proposed. The existence of the first moment for any summand is not assumed. The assumption of independence is understood in the nonlinear sense, and may be further a little relaxed.