An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter

We consider fractional Brownian motions BtH with arbitrary Hurst coefficients 0<H<1 and prove the following results: (i) An integral representation of the fractional white noise as generalized Wiener integral; (ii) an Itô formula for generalized functionals of BtH; (iii) an analogue of Tanaka's formula; (iv) a Clark-Ocone formula for Donsker's delta function of BtH; (v) an integral representation of the local time of BtH.

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Year of publication:	2003
Authors:	Bender, Christian
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 104.2003, 1, p. 81-106
Publisher:	Elsevier
Keywords:	Fractional Brownian motion Fractional white noise Ito formula Tanaka formula Local time Unified treatment for arbitrary Hurst parameter

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

Persistent link: https://www.econbiz.de/10008875746