| 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 ORBilu) |
| 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 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 |
| 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 |