AN EXTENSION OF THE LEVY CHARACTERIZATION TO FRACTIONAL BROWNIAN MOTION

被引：4
|
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.
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页码：439 / 470
页数：32
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