Limit theorems for nonlinear functionals of Volterra processes via white noise analysis

被引：7

作者：

Darses, Sebastien ^{[1
]}

Nourdin, Ivan ^{[2
]}

Nualart, David ^{[3
]}

机构：

[1] Univ Aix Marseille 1, F-13453 Marseille 13, France

[2] Univ Paris 06, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France

[3] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

BERNOULLI | 2010年 / 16卷 / 04期

基金：

美国国家科学基金会;

关键词：

fractional Brownian motion; limit theorems; Volterra processes; white noise analysis; FRACTIONAL BROWNIAN-MOTION; MULTIPLE STOCHASTIC INTEGRALS; GAUSSIAN-PROCESSES; CONVERGENCE; CALCULUS; FIELDS; CLT;

D O I：

10.3150/10-BEJ258

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：

By means of white noise analysis, we prove some limit theorems for nonlinear functionals of a given Volterra process. In particular, our results apply to fractional Brownian motion (fBm) and should be compared with the classical convergence results of the 1980s due to Breuer, Dobrushin, Giraitis, Major, Surgailis and Taqqu, as well as the recent advances concerning the construction of a Levy area for fBm due to Coutin, Qian and Unterberger.

引用

页码：1262 / 1293

页数：32

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