STOCHASTIC INTEGRATION FOR FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE-Reference-Cited by-同舟云学术

STOCHASTIC INTEGRATION FOR FRACTIONAL BROWNIAN MOTION IN A HILBERT SPACE

Published:2006-03 Issue:01 Volume:06 Page:53-75
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

DUNCAN T. E.¹,JAKUBOWSKI J.²,PASIK-DUNCAN B.¹

Affiliation:

1. Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA

2. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland

Abstract

A Hilbert space-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space and an operator-valued integrand. Since the integrator is not a semimartingale for the fractional Brownian motions that are considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach uses some ideas from Malliavin calculus. In addition to the definition of stochastic integration, an Itô formula is given for smooth functions of some processes that are obtained by the stochastic integration.

Publisher

World Scientific Pub Co Pte Lt

Subject

Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493706001645

Reference21 articles.

1. Stochastic Calculus with Respect to Gaussian Processes

2. Stochastic integration with respect to the fractional Brownian motion

3. The Skorohod integral in conuclear spaces

4. Itô's formula with respect to fractional Brownian motion and its application

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