On quantitative bounds in the mean martingale central limit theorem

TL;DR

This paper derives explicit bounds on how close the distribution of discrete time martingales is to the normal distribution using Wasserstein distance, combining Lindeberg's and Stein's methods.

Contribution

It introduces new explicit bounds on the Wasserstein distance for discrete martingales to the normal distribution, enhancing understanding of convergence rates.

Findings

Explicit Wasserstein bounds for martingales to normal distribution

Combination of Lindeberg's and Stein's methods for proofs

Improved quantitative understanding of martingale CLT

Abstract

We provide explicit bounds on the Wasserstein distance between discrete time martingales and the standard normal distribution. The proofs are based on a combination of Lindeberg's and Stein's method.