Rate estimates for total variation distance with applications

TL;DR

This paper introduces a Fourier-analytic approach to estimate convergence rates in total variation distance, with applications in Malliavin calculus, normal approximation, and stochastic dynamical systems with memory.

Contribution

It develops a novel Fourier-analytic method for bounding total variation convergence rates, connecting weak convergence metrics with practical applications.

Findings

Provides explicit convergence rate estimates in total variation

Applies method to Malliavin calculus and normal approximation

Demonstrates effectiveness in stochastic systems with memory

Abstract

We present a Fourier-analytic method for estimating convergence rates in total variation distance in terms of various metrics related to weak convergence. Applications are provided in the areas of Malliavin calculus, normal approximation and stochastic dynamical systems with memory.