Quantitative Fourth Moment Theorem of Functions on the Markov Triple and Orthogonal Polynomials
In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple E,μ,Γ, where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9408651 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple E,μ,Γ, where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the random variable of a general Markov diffusion generator, not necessarily belonging to a fixed eigenspace, while previous works deal with only random variables to belong to a fixed eigenspace. As this technique will be applied to the works studied by Bourguin et al. (2019), we obtain the new result in the case where the chaos grade of an eigenfunction of Markov diffusion generator is greater than two. Also, we introduce the chaos grade of a new notion, called the lower chaos grade, to find a better estimate than the previous one. |
|---|---|
| ISSN: | 2314-8896 2314-8888 |