Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Nualart, David²  Saussereau, Bruno¹ 

[1] UMR CNRS 6623, Lab Math Besancon, F-25030 Besancon, France

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

关键词: Stochastic differential equation;    Malliavin calculus;    Fractional Brownian motion;   

DOI  :  10.1016/j.spa.2008.02.016

来源: Elsevier

【 摘 要 】

We prove the Malliavin regularity of the solution of a stochastic differential equation driven by a fractional Brownian motion of Hurst parameter H > 0.5. The result is based on the Frechet differentiability with respect to the input function for deterministic differential equations driven by Wider Continuous functions. It is also shown that the law of the solution has a density with respect to the Lebesgue measure, tinder a Suitable nondegeneracy condition. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

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