A frequency domain approach to some results on fractional Brownian motion

Let X be a fractional Brownian motion. It is known that Mt=[integral operator]mt dX, t[greater-or-equal, slanted]0, where mt is a certain kernel, defines a martingale M, and also that X can be represented by Xt=[integral operator]xt dM, t[greater-or-equal, slanted]0, for some kernel xt. We derive these results by using the spectral representation of the covariance function of X. A formula for the covariance between X and M is also given.

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Year of publication:	2002
Authors:	Dzhaparidze, K. ; Ferreira, J. A.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 60.2002, 2, p. 155-168
Publisher:	Elsevier
Keywords:	Fractional Brownian motion Integral transforms Spectral representation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005137955