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March 2011 An extension of the Lévy characterization to fractional Brownian motion
Yuliya Mishura, Esko Valkeila
Ann. Probab. 39(2): 439-470 (March 2011). DOI: 10.1214/10-AOP555

Abstract

Assume that X is a continuous square integrable process with zero mean, defined on some probability space (Ω, F, P). The classical characterization due to P. Lévy says that X is a Brownian motion if and only if X and Xt2t, t ≥ 0, are martingales with respect to the intrinsic filtration FX. We extend this result to fractional Brownian motion.

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Yuliya Mishura. Esko Valkeila. "An extension of the Lévy characterization to fractional Brownian motion." Ann. Probab. 39 (2) 439 - 470, March 2011. https://doi.org/10.1214/10-AOP555

Information

Published: March 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1227.60051
MathSciNet: MR2789503
Digital Object Identifier: 10.1214/10-AOP555

Subjects:
Primary: 60G15
Secondary: 60E05 , 60H99

Keywords: fractional Brownian motion , Lévy theorem

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • March 2011
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