FRACTIONAL MARTINGALES AND CHARACTERIZATION OF THE FRACTIONAL BROWNIAN MOTION
成果类型：
Article
署名作者：
Hu, Yaozhong; Nualart, David; Song, Jian
署名单位：
University of Kansas
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/09-AOP464
发表日期：
2009
页码：
2404-2430
关键词：
摘要：
In this paper we introduce the notion of fractional martingale as the fractional derivative of order a of a continuous local martingale, where alpha is an element of (-1/2, 1/2) and we show that it has a nonzero finite variation of order 2/1+2 alpha, under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Levy's characterization theorem for the fractional Brownian motion.