Work

The optimal fourth moment theorem

Year: 2013

Type: article

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.

DOI: 10.48550/arxiv.1305.1527

Authors: Nourdin, Ivan, Peccati, Giovanni

Institutions: Institut Élie Cartan de Lorraine, Université de Lorraine, University of Luxembourg

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W2952953370

FWCI: 0.582

Cites: 16

Cited by: 1

Related to: 10