An \(S\)-transform approach to integration with respect to a fractional Brownian motion
type: Item
instance of: scholarly article
title: An \(S\)-transform approach to integration with respect to a fractional Brownian motion
zbMATH Open document ID: 1047.60049
author: Christian Bender
published in: Bernoulli
publication date: 2004-06-10T00:00:00Z
review text: An elementary definition of the (Wick)-Itô integral is given with respect to a fractional Brownian motion using the expectation, the ordinary Lebesgue integral and the classical (simple) Wiener integral. The expectation of the fractional Itô integral under change of measure is calculated and a Girsanov theorem for the fractional Itô integral is proven (not only for fractional Brownian motion). An Itô formula for functionals of a fractional Wiener integral is derived.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 2072447
zbMATH Keywords: change of measure
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: fractional Girsanov theorem
zbMATH Keywords: fractional Itô integral
zbMATH Keywords: \(S\)-transform
reviewed by: Rózsa Horváth-Bokor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3150/bj/1072215197
OpenAlex ID: W2007642833
DOI: 10.3150/BJ/1072215197
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description: scientific article; zbMATH DE number 2072447