Four moments theorems on Markov chaos

Bourguin, Solesne, Campese, Simon, Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Taqqu, Murad S. 2019. Four moments theorems on Markov chaos. Annals of Probability 47 (3) , pp. 1417-1446. 10.1214/18-AOP1287

Preview

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

Abstract

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:	21 Nov 2024 00:00
URI:	https://orca.cardiff.ac.uk/id/eprint/111434

Citation Data

Cited 6 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item