Normal approximation when a chaos grade is greater than two

Yoon Tae Kim and Hyun Suk Park

Statistics & Probability Letters, 2022, vol. 185, issue C

Abstract: We derive an upper bound on a probabilistic distance for a normal approximation when the chaos grade of an eigenfunction of Markov diffusion generator L is greater than 2. When a chaos grade is strictly greater than 2, the upper bound, given by Bourguin et al. (2019), does not guarantee that Fn converges in distribution to a standard Gaussian distribution even when the fourth cumulant of Fn converges to 0. This means that the fourth moment theorem, discovered by Nualart and Peccati (2005), does not work. In this paper, we develop a new technique to obtain an upper bound for which the fourth moment theorem works when a chaos grade is strictly greater than 2.

Keywords: Markov diffusion generator; Fourth moment theorem; Markov chaos; Carré du champ operator; Chaos grade (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715222000141
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:185:y:2022:i:c:s0167715222000141

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2022.109389

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().