AN EXTENSION OF THE LEVY CHARACTERIZATION TO FRACTIONAL BROWNIAN MOTION

被引：6

作者：

Mishura, Yuliya ^{[1
]}

Valkeila, Esko ^{[2
]}

机构：

[1] Kiev Univ, Dept Math, UA-01033 Kiev, Ukraine

[2] Aalto Univ, Dept Math & Syst Anal, FI-00076 Aalto, Finland

来源：

ANNALS OF PROBABILITY | 2011年 / 39卷 / 02期

关键词：

Fractional Brownian motion; Levy theorem;

D O I：

10.1214/10-AOP555

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：

Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Omega, F, P). The classical characterization due to P. Levy says that X is a Brownian motion if and only if X and X-t(2) - t, t >= 0, are martingales with respect to the intrinsic filtration F-X. We extend this result to fractional Brownian motion.

引用

页码：439 / 470

页数：32

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