In this paper we introduce the notion of fractional martingale as the fractional derivative of order α of a continuous local martingale, where α∈(−½, ½), and we show that it has a nonzero finite variation of order 2/(1+2α), under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Lévy’s characterization theorem for the fractional Brownian motion.
@article{1258380793,
author = {Hu, Yaozhong and Nualart, David and Song, Jian},
title = {Fractional martingales and characterization of the fractional Brownian motion},
journal = {Ann. Probab.},
volume = {37},
number = {1},
year = {2009},
pages = { 2404-2430},
language = {en},
url = {http://dml.mathdoc.fr/item/1258380793}
}
Hu, Yaozhong; Nualart, David; Song, Jian. Fractional martingales and characterization of the fractional Brownian motion. Ann. Probab., Tome 37 (2009) no. 1, pp. 2404-2430. http://gdmltest.u-ga.fr/item/1258380793/