Weak approximation of a fractional SDE

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Bardina, X.²  Nourdin, I.³  Rovira, C.¹  Tindel, S.⁴ 

[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

关键词: Weak approximation;    Kac-Stroock type approximation;    Fractional Brownian motion;    Rough paths;   

DOI  :  10.1016/j.spa.2009.10.008

来源: Elsevier

【 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.

【 授权许可】

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