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November 2009 Fractional martingales and characterization of the fractional Brownian motion
Yaozhong Hu, David Nualart, Jian Song
Ann. Probab. 37(6): 2404-2430 (November 2009). DOI: 10.1214/09-AOP464

Abstract

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.

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Yaozhong Hu. David Nualart. Jian Song. "Fractional martingales and characterization of the fractional Brownian motion." Ann. Probab. 37 (6) 2404 - 2430, November 2009. https://doi.org/10.1214/09-AOP464

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1196.60075
MathSciNet: MR2573562
Digital Object Identifier: 10.1214/09-AOP464

Subjects:
Primary: 26A45, 60G15, 60G44, 60J65

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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