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.

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页数：10

相关论文

共 30 条

[1] A UNIFORM CENTRAL-LIMIT-THEOREM FOR SET-INDEXED PARTIAL-SUM PROCESSES WITH FINITE VARIANCE [J].

ALEXANDER, KS ;

PYKE, R .

ANNALS OF PROBABILITY, 1986, 14 (02) :582-597

[2] Approximation of the finite dimensional distributions of multiple fractional integrals [J].

Bardina, Xavier ;

Es-Sebaiy, Khalifa ;

Tudor, Ciprian A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (02) :694-711

[3] On the convergence to the multiple Wiener-Ito integral [J].

Bardina, Xavier ;

Jolis, Maria ;

Tudor, Ciprian A. .

BULLETIN DES SCIENCES MATHEMATIQUES, 2009, 133 (03) :257-271

[4] INVARIANCE PRINCIPLES FOR SELF-SIMILAR SET-INDEXED RANDOM FIELDS [J].

Bierme, Hermine ;

Durieu, Olivier .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 366 (11) :5963-5989

[5]

Billingsley Patrick, 1999, CONVERGE PROBAB MEAS, DOI DOI 10.1002/9780470316962

[6]

Bogachev V.I., 2007, Measure Theory, VI

[7] Central limit theorem for multiple integrals with respect to the empirical process [J].

Boistard, Helene ;

del Barrio, Eustasio .

STATISTICS & PROBABILITY LETTERS, 2009, 79 (02) :188-195

[8]

Bryc Wlodzimierz, 1995, Demonstratio Math., V28, P733

[9]

Budhiraja A, 1997, STAT SINICA, V7, P907

[10] THE EMPIRICAL PROCESS OF SOME LONG-RANGE DEPENDENT SEQUENCES WITH AN APPLICATION TO U-STATISTICS [J].

DEHLING, H ;

TAQQU, MS .

ANNALS OF STATISTICS, 1989, 17 (04) :1767-1783