Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Four moments theorems on Markov chaos

Bourguin, Solesne, Campese, Simon, Leonenko, Nikolai and Taqqu, Murad S. 2019. Four moments theorems on Markov chaos. Annals of Probability 47 (3) , pp. 1417-1446. 10.1214/18-AOP1287

PDF - Accepted Post-Print Version
Download (648kB) | Preview


We obtain quantitative Four Moments Theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumptionwe make on the Pearson distribution is that it admits four moments. These results are obtained by rst proving a general carré du champ bound on the distance between laws of random variables in the domain of a Markov diusion generator and invariant measures of diusions, which is of independent interest, and making use of the new concept of chaos grade. For the heavy-tailed Pearson distributions, this seems to be the rst time that sucient conditions in terms of (nitely many) moments are given in order to converge to a distribution that is not characterized by its moments.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Institute of Mathematical Statistics
ISSN: 0091-1798
Date of First Compliant Deposit: 14 May 2018
Date of Acceptance: 10 May 2018
Last Modified: 18 Jan 2021 19:58

Actions (repository staff only)

Edit Item Edit Item


Downloads per month over past year

View more statistics