On Gaussian processes equivalent in law to fractional Brownian motion

被引：8

作者：

Sottinen, T

机构：

[1] Univ Helsinki, Dept Math, FIN-00014 Helsinki, Finland

[2] Univ Aarhus, DK-8000 Aarhus C, Denmark

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2004年 / 17卷 / 02期

关键词：

Fractional Brownian motion; equivalence of Gaussian processes; Hitsuda representation; canonical representation of Gaussian processes; Girsanov theorem; stochastic differential equations;

D O I：

10.1023/B:JOTP.0000020696.99064.5d

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：

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H less than or equal to 1/2. For the case H > 1/2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation we consider a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise.

引用

页码：309 / 325

页数：17

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