On Gaussian processes equivalent in law to fractional Brownian motion
type: Item
instance of: scholarly article
title: On Gaussian processes equivalent in law to fractional Brownian motion
zbMATH Open document ID: 1049.60030
published in: Journal of Theoretical Probability
publication date: 2004-08-06T00:00:00Z
review text: This paper considers Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. The paper proves a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index \(H\leq \frac{1}{2}\). For the case \(H>\frac{1}{2}\) it is shown that such a representation cannot hold. The paper also considers briefly the connection between Hitsuda and Girsanov representations. Using the Hitsuda representation the paper considers a certain special kind of Gaussian stochastic equation with fractional Brownian motion as noise.
reviewed by: Yuhu Feng
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 2083449
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: equivalence of Gaussian processes
zbMATH Keywords: Hitsuda representation
zbMATH Keywords: canonical representation of Gaussian processes
zbMATH Keywords: Girsanov theorem
zbMATH Keywords: stochastic differential equations
author: Tommi Sottinen
MaRDI profile type: Publication
full work available at URL: b:jotp.0000020696.99064.5d
OpenAlex ID: W1970549031
DOI: 10.1023/B:JOTP.0000020696.99064.5D
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description: scientific article; zbMATH DE number 2083449