FOUR MOMENTS THEOREMS ON MARKOV CHAOS

• 成果类型: Article
• 署名作者: Bourguin, Solesne; Campese, Simon; Leonenko, Nikolai; Taqqu, Murad S.
• 署名单位: Boston University; University of Luxembourg; Cardiff University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1287
• 发表日期: 2019
• 页码: 1417-1446
• 关键词: CENTRAL LIMIT-THEOREMS; DIFFUSIONS

摘要

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 carre 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.