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Four moments theorems for Markov chaos

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

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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: Published Online
Status: Published
Schools: Mathematics
Publisher: Institute of Mathematical Statistics (IMS)
ISSN: 0091-1798
Date of First Compliant Deposit: 14 May 2018
Date of Acceptance: 10 May 2018
Last Modified: 01 Jul 2019 09:17
URI: http://orca.cf.ac.uk/id/eprint/111434

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