Empirical limit theorems for Wiener chaos

被引：0

作者：

Bai, Shuyang ^{[1
]}

Chen, Jiemiao ^{[1
]}

机构：

[1] Univ Georgia, 310 Herty Dr, Athens, GA 30602 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 215卷

关键词：

Limit theorems; Wiener chaos; Multiple stochastic integrals; Empirical measure; Gaussian random measure; STOCHASTIC INTEGRALS; MULTIPLE; APPROXIMATION; CONVERGENCE; RESPECT;

D O I：

10.1016/j.spl.2024.110222

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 consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener-Ito integrals are established.

引用

页数：10

共 30 条

[11]

DEHLING H, 2002, EMPIRICAL PROCESS TE, P3

[12] SYMMETRIC STATISTICS, POISSON POINT-PROCESSES, AND MULTIPLE WIENER INTEGRALS [J].