Reference : Four Moments Theorems on Markov Chaos
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Four Moments Theorems on Markov Chaos
Bourguin, Solesne [Boston University > Department of Mathematics and Statistics]
Campese, Simon mailto [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]
Annals of Probability
Institute of Mathematical Statistics
Yes (verified by ORBilu)
[en] Markov Operator ; Stein's method ; Gamma calculus ; Pearson distribution ; limit theorems ; diffusion generator
[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.
Fonds National de la Recherche - FnR
FnR ; FNR11590883 > Simon Campese > LILAC > Limit and Law Characterizations for Chaotic Random Variables > 01/09/2017 > 01/06/2018 > 2017

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