Approximation of the finite dimensional distributions of multiple fractional integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Bardina, Xavier²  Es-Sebaiy, Khalifa³  Tudor, Ciprian A.¹ 

[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

关键词: Multiple stochastic integrals;    Limit theorems;    Fractional Brownian motion;    Weak convergence;   

DOI  :  10.1016/j.jmaa.2010.04.009

来源: Elsevier

【 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.

【 授权许可】

Free