| Four Moments Theorems on Markov Chaos |

| English |

| 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]* |

| 2019 |

| Annals of Probability |

| Institute of Mathematical Statistics |

| 47 |

| 3 |

| 1417-1446 |

| Yes (verified by ORBi^{lu}) |

| 0091-1798 |

| 2168-894X |

| Beachwood |

| OH |

| [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 carrĂ© 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 |

| http://hdl.handle.net/10993/42066 |

| 10.1214/18-AOP1287 |

| https://dx.doi.org/10.1214/18-AOP1287 |

| FnR ; FNR11590883 > Simon Campese > LILAC > Limit and Law Characterizations for Chaotic Random Variables > 01/09/2017 > 01/06/2018 > 2017 |