FOUR MOMENTS THEOREMS ON MARKOV CHAOS

被引：7

作者：

Bourguin, Solesne ^{[1
]}

Campese, Simon ^{[2
]}

Leonenko, Nikolai ^{[3
]}

Taqqu, Murad S. ^{[1
]}

机构：

[1] Boston Univ, Dept Math & Stat, 111 Cummington Mall, Boston, MA 02215 USA

[2] Univ Luxembourg, Math Res Unit, 6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg

[3] Cardiff Univ, Sch Math, Senghennydd Rd, Cardiff CF24 4AG, S Glam, Wales

来源：

ANNALS OF PROBABILITY | 2019年 / 47卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Markov operator; diffusion generator; Gamma calculus; Pearson distributions; Stein's method; limit theorems; CENTRAL LIMIT-THEOREMS; DIFFUSIONS;

D O I：

10.1214/18-AOP1287

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：1417 / 1446

页数：30

共 20 条

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[4] MATRIX CALCULATIONS FOR MOMENTS OF MARKOV PROCESSES
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[9] Kolmogorov distance for the central limit theorems of the Wiener chaos expansion and applications
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