Probability asymptotics: notes on notation

TL;DR

This paper reviews various asymptotic notations for sequences of random variables, clarifying their definitions and relationships to aid future research, despite their elementary and well-known nature.

Contribution

It compiles and clarifies different versions of asymptotic notations for random variables for easier reference and application.

Findings

Different versions of O and o for random variables are compared.

Elementary results are summarized for future use.

The paper serves as a reference for asymptotic notation in probability theory.

Abstract

Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future use and easy reference.