[en] 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.
Disciplines :
Mathématiques
Auteur, co-auteur :
Bourguin, Solesne; Boston University > Department of Mathematics and Statistics
CAMPESE, Simon ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Leonenko, Nikolai; Cardiff University > School of Mathematics
Taqqu, Murad; Boston University > Department of Mathematics and Statistics
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Four Moments Theorems on Markov Chaos
Date de publication/diffusion :
2019
Titre du périodique :
Annals of Probability
ISSN :
0091-1798
eISSN :
2168-894X
Maison d'édition :
Institute of Mathematical Statistics, Beachwood, Etats-Unis - Ohio
