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Licensed Unlicensed Requires Authentication Published by De Gruyter August 21, 2014

Fractional white noise calculus in infinite dimensions

  • Wilfried Grecksch EMAIL logo and Christian Roth

Abstract

In this paper we consider a white noise calculus for fractional Brownian motion with values in a separable Hilbert space, whereby the covariance operator Q is a kernel operator (Q-fractional Brownian motion). We prove a Q-fractional version of the Itô's formula. Furthermore, we introduce Malliavin derivative for Q-fractional motion, prove a Q-fractional integration-by-parts formula and a Q-fractional version of the Itô isometry.

MSC: 60H15; 60H40
Received: 2012-5-1
Accepted: 2014-5-5
Published Online: 2014-8-21
Published in Print: 2014-9-1

© 2014 by De Gruyter

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