Abstract

The purpose of this note is to survey some recent developments in the applications of Malliavin calculus combined with Stein’s method to derive central limit theorems for random variables on a finite sum of Wiener chaos. Starting from the fourth moment theorem by Nualart and Peccati [23], we will discuss several related topics such as conditions for the convergence in total variation, absolute continuity of probability laws and uniform convergence of densities under suitable non degeneracy assumptions. The fact that the random variables belong to a fixed Wiener chaos (or to a finite sum of Wiener chaos) will play a fundamental role in the results.

Full Text
Paper version not known

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

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.