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VOL. 5 | 2009 Conditional expectations and martingales in the fractional Brownian field
Vladimir Dobrić, Francisco M. Ojeda

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad


Conditional expectations of a fractional Brownian motion with Hurst index H respect to the filtration of a fractional Brownian motion with Hurst index H, both contained in the fractional Brownian field, are studied. A stochastic integral representation of those processes is constructed from the covariance structure of the underlying fractional Brownian field. As processes, the conditional expectations contain martingale components and for dual pairs of Hurst indices the processes become pure martingales which, up to a multiplicative constant, coincide with the fundamental martingales of fractional Brownian motions.


Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60037
MathSciNet: MR2797950

Digital Object Identifier: 10.1214/09-IMSCOLL515

Primary: 60G15
Secondary: 60G18 , 60G44

Keywords: fractional Brownian field , fractional Brownian motions , fundamental martingales

Rights: Copyright © 2009, Institute of Mathematical Statistics


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