Weak approximation of a fractional SDE

被引：7

作者：

Bardina, X. ^{[2
]}

Nourdin, I. ^{[3
]}

Rovira, C. ^{[1
]}

Tindel, S. ^{[4
]}

机构：

[1] Univ Barcelona, Fac Matemat, E-08007 Barcelona, Spain

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

[3] Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 5, France

[4] Inst Elie Cartan Nancy, F-54506 Vandoeuvre Les Nancy, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 01期

关键词：

Weak approximation; Kac-Stroock type approximation; Fractional Brownian motion; Rough paths; ROUGH PATH-ANALYSIS; BROWNIAN-MOTION; GAUSSIAN-PROCESSES; LARGE DEVIATIONS; EQUATIONS; CALCULUS; INTEGRALS; DRIVEN;

D O I：

10.1016/j.spa.2009.10.008

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：

In this note, a diffusion approximation result is shown for stochastic differential equations driven by a (Liouville) fractional Brownian motion B with Hurst parameter H is an element of (1/3, 1/2). More precisely, we resort to the Kac-Stroock type approximation using a Poisson process studied in Bardina et al. (2003) [4] and Delgado and Jolis (2000) [9], and our method of proof relies on the algebraic integration theory introduced by Gubinelli in Gubinelli (2004) [14]. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：39 / 65

页数：27

共 33 条

[1]

Adams A., 2003, Sobolev Spaces, V140

[2] Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2 [J].

Alòs, E ;

Mazet, O ;

Nualart, D .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2000, 86 (01) :121-139

[3]

Alòs E, 2001, TAIWAN J MATH, V5, P609

[4] Convergence in law to the multiple fractional integral [J].

Bardina, X ;

Jolis, M ;

Tudor, CA .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2003, 105 (02) :315-344

[5]

BARDINA X, 2008, ARXIV07090805V2

[6] Operators associated with a stochastic differential equation driven by fractional Brownian motions [J].

Baudoin, Fabrice ;

Coutin, Laure .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (05) :550-574

[7] FROM RANDOM WALKS TO ROUGH PATHS [J].

Breuillard, Emmanuel ;

Friz, Peter ;

Huesmann, Martin .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (10) :3487-3496

[8] Stochastic analysis, rough path analysis and fractional Brownian motions [J].

Coutin, L ;

Qian, ZM .

PROBABILITY THEORY AND RELATED FIELDS, 2002, 122 (01) :108-140

[9] Weak approximation for a class of Gaussian processes [J].

Delgado, R ;

Jolis, M .

JOURNAL OF APPLIED PROBABILITY, 2000, 37 (02) :400-407

[10] On fractional Brownian processes [J].

Feyel, D ;

De la Pradelle, A .

POTENTIAL ANALYSIS, 1999, 10 (03) :273-288

← 1 2 3 4 →