## Abstract

We compute the exact rates of convergence in total variation associated with the ‘fourth moment theorem’ by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.

## Full Text

Sign-in/Register to access full text options

### Topics from this Paper

- Fourth Moment Theorem
- Convergence In Total Variation
- Central Limit Theorem
- Convergence In Variation
- Optimal Moment + Show 5 more

Create a personalized feed of these topics

Get Started#### Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call### Similar Papers

Characterization of the convergence in total variation and extension of the Fourth Moment Theorem to invariant measures of diffusions

- Bernoulli
- May 1, 2018

Relevant

Not Relevant

Entropy and the fourth moment phenomenon

- Journal of Functional Analysis
- Mar 1, 2014

Relevant

Not Relevant

Absolute continuity and convergence of densities for random vectors on Wiener chaos

- Electronic Journal of Probability
- Jan 1, 2013

Relevant

Not Relevant

Local Limit Theorems for Densities in Orlicz Spaces

- Journal of Mathematical Sciences
- Aug 17, 2019

Relevant

Not Relevant

Regularization lemmas and convergence in total variation

- Electronic Journal of Probability
- Jan 1, 2020

Relevant

Not Relevant

Distribution estimation consistent in total variation and in two types of information divergence

- IEEE Transactions on Information Theory
- Jan 1, 1992

Relevant

Not Relevant

Stochastic annealing for nearest-neighbour point processes with application to object recognition

- Advances in Applied Probability
- Jun 1, 1994

Relevant

Not Relevant

Stochastic annealing for nearest-neighbour point processes with application to object recognition

- Advances in Applied Probability
- Jun 1, 1994

Relevant

Not Relevant

Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem

- Dec 15, 2014

Relevant

Not Relevant

Fisher information and the fourth moment theorem

- Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
- May 1, 2016

Relevant

Not Relevant

Function-Specific Mixing Times and Concentration Away from Equilibrium

- Bayesian Analysis
- Jun 1, 2020

Relevant

Not Relevant

Multivariate normal approximation for traces of random unitary matrices

- The Annals of Probability
- Nov 1, 2021

Relevant

Not Relevant

READ MORE FROM

### Proceedings of the American Mathematical Society

An optimal approximation problem for free polynomials

Open Access

Just Published

- Proceedings of the American Mathematical Society
- Nov 17, 2023

Relevant

Not Relevant

Categorical properties of reduction functors over non-positive DG-rings

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Contractibility of the orbit space of the p-subgroup complex via Brown-Forman discrete Morse theory

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Conformal flatness of compact three-dimensional Cotton-parallel manifolds

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Sufficient condition for compactness of the \overline{∂}-Neumann operator using the Levi core

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

The Borel partition spectrum at successors of singular cardinals

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

A note on the convex body isoperimetric conjecture in the plane

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Optimal diameter estimate of three-dimensional Ricci limit spaces

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Global asymptotic stability for Gurtin-MacCamy’s population dynamics model

Open Access

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant

Two results on x^{r}+y^{r}=dz^{p}

- Proceedings of the American Mathematical Society
- Nov 7, 2023

Relevant

Not Relevant