Stochastic analysis of the fractional Brownian motion
type: Item
instance of: scholarly article
title: Stochastic analysis of the fractional Brownian motion
zbMATH Open document ID: 0924.60034
DOI: 10.1023/A:1008634027843
author: Laurent Decreusefond
author: A. S. Üstünel
published in: Potential Analysis
publication date: 1999-07-20T00:00:00Z
review text: Since the fractional Brownian motion (fBm) is not a semimartingale, the usual stochastic calculus cannot be used to analyze it; however since it is a Gaussian process, the authors have applied the stochastic calculus of variations which is valid on general Wiener spaces. By using some well-known properties of the standard Brownian motion, the authors obtain the Itô-Clark representation formula. By an intrinsic analysis of the fBm, they obtain the Itô formula and the Girsanov theorem. Throughout the paper, they give two practical applications such as the simulation of sample-paths of the fBm and an estimation problem involving an fBm.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60G18
zbMATH DE Number: 1286664
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: stochastic calculus of variations
zbMATH Keywords: Itô formula
zbMATH Keywords: Girsanov formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1286664