Stochastic integration with respect to fractional Brownian motion

被引：81

作者：

Carmona, P

Coutin, L

Montseny, G

机构：

[1] Univ Toulouse 3, Lab Stat & Probabil, F-31062 Toulouse 4, France

[2] LAAS, F-31077 Toulouse, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2003年 / 39卷 / 01期

关键词：

Gaussian processes; stochastic integrals; malliavin calculus; fractional integration;

D O I：

10.1016/S0246-0203(02)01111-1

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：

For every value of the Hurst index H is an element of (0, 1) we define a stochastic integral with respect to fractional Brownian motion of index H. We do so by approximating fractional Brownian motion by semi-martingales. Then, for H > 1/6 we establish an W's change of variables formula, which is more precise than Privault's Ito formula (1998) (established for every H > 0), since it only involves anticipating integrals with respect to a driving Brownian motion. 2003 Editions scientifiques et medicales Elsevier SAS.

引用

页码：27 / 68

页数：42

共 34 条

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