Stochastic integration with respect to the fractional Brownian motion

Author: Alòs Elisa  

Publisher: Taylor & Francis Ltd

ISSN: 1045-1129

Source: Stochastics and Stochastics Reports, Vol.75, Iss.3, 2003-01, pp. : 129-152

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Abstract

We develop a stochastic calculus for the fractional Brownian motion with Hurst parameter H>1/2 using the techniques of the Malliavin calculus. We establish estimates in Lp, maximal inequalities and a continuity criterion for the stochastic integral. Finally, we derive an Itô's formula for integral processes.