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May 2019 Four moments theorems on Markov chaos
Solesne Bourguin, Simon Campese, Nikolai Leonenko, Murad S. Taqqu
Ann. Probab. 47(3): 1417-1446 (May 2019). DOI: 10.1214/18-AOP1287

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 assumption we make on the Pearson distribution is that it admits four moments. These results are obtained by first proving a general carré du champ bound on the distance between laws of random variables in the domain of a Markov diffusion generator and invariant measures of diffusions, 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 first time that sufficient conditions in terms of (finitely many) moments are given in order to converge to a distribution that is not characterized by its moments.

Citation

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Solesne Bourguin. Simon Campese. Nikolai Leonenko. Murad S. Taqqu. "Four moments theorems on Markov chaos." Ann. Probab. 47 (3) 1417 - 1446, May 2019. https://doi.org/10.1214/18-AOP1287

Information

Received: 1 December 2017; Revised: 1 March 2018; Published: May 2019
First available in Project Euclid: 2 May 2019

zbMATH: 07067273
MathSciNet: MR3945750
Digital Object Identifier: 10.1214/18-AOP1287

Subjects:
Primary: 60F05, 60J35, 60J99

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 3 • May 2019
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