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Fractional Integral Equations and State Space Transforms

Buchmann, Boris; Klueppelberg, Claudia C

Description

We introduce a class of stochastic differential equations driven by fractional Brownian motion which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extension of the fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated, and their stationary densities are explicitly given.

dc.contributor.authorBuchmann, Boris
dc.contributor.authorKlueppelberg, Claudia C
dc.date.accessioned2015-12-07T22:41:33Z
dc.identifier.issn1350-7265
dc.identifier.urihttp://hdl.handle.net/1885/24366
dc.description.abstractWe introduce a class of stochastic differential equations driven by fractional Brownian motion which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extension of the fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated, and their stationary densities are explicitly given.
dc.publisherChapman & Hall
dc.sourceBernoulli
dc.subjectKeywords: Fractional Brownian motion; Fractional integral; Fractional Ornstein-Uhlenbeck process; Fractional Vasicek model; Langevin equation; Long-range dependence; Riemann-Stieltjes integrals; Solution of stochastic differential equations; State space transform;
dc.titleFractional Integral Equations and State Space Transforms
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume12
dc.date.issued2006
local.identifier.absfor010406 - Stochastic Analysis and Modelling
local.identifier.ariespublicationu3488905xPUB32
local.type.statusPublished Version
local.contributor.affiliationBuchmann, Boris, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationKlueppelberg, Claudia C, Munich University of Technology
local.description.embargo2037-12-31
local.bibliographicCitation.issue3
local.bibliographicCitation.startpage431
local.bibliographicCitation.lastpage456
local.identifier.doi10.3150/bj/1151525129
dc.date.updated2015-12-07T11:02:22Z
local.identifier.scopusID2-s2.0-33846108890
CollectionsANU Research Publications

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