Approximation of the finite dimensional distributions of multiple fractional integrals

被引：3

作者：

Bardina, Xavier ^{[2
]}

Es-Sebaiy, Khalifa ^{[3
]}

Tudor, Ciprian A. ^{[1
]}

机构：

[1] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

[2] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Barcelona, Spain

[3] Univ Paris 01, SAMM, F-75634 Paris, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 369卷 / 02期

关键词：

Multiple stochastic integrals; Limit theorems; Fractional Brownian motion; Weak convergence; WEAK-CONVERGENCE;

D O I：

10.1016/j.jmaa.2010.04.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a family I-n, < f >(t) of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener-Ito integral I-n(H)(f1(vertical bar 0,t vertical bar)(circle times n)) with respect to the fractional Brownian motion. We assume that H > 1/2 and we prove our approximation result for the integrands f in a rather general class. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：694 / 711

页数：18

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