Skip to main content
Create account Takes you to the ID+ sign in page Sign in
Applied Mathematics and OptimizationVolume 57, Issue 3, June 2008, Pages 401-429

Ergodicity and parameter estimates for infinite-dimensional fractional ornstein-uhlenbeck process(Article)(Open Access)

  Save all to author list
  • aInstitute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic
  • bFaculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Abstract

Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise. © 2007 Springer Science+Business Media, LLC.

Author keywords

ErgodicityFractional Brownian motionFractional Ornstein-Uhlenbeck processParameter estimatesStochastic partial differential equationsStrictly stationary solution

Indexed keywords

Engineering uncontrolled termsErgodicityFractional Brownian motionOrnstein-Uhlenbeck processStrictly stationary solution
Engineering controlled terms:Acoustic noiseBrownian movementParameter estimationPartial differential equations
Engineering main heading:Linear equations

Funding details

Funding sponsor Funding number Acronym
MSM 4977751301
Grantová Agentura České Republiky201/04/0750GA ČR

  • 1

    This work was partially supported by the GACR Grant 201/04/0750 and by the MSMT Research Plan MSM 4977751301.

  • ISSN: 00954616
  • CODEN: AMOMB
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1007/s00245-007-9028-3
  • Document Type: Article

  Maslowski, B.; Institute of Mathematics, Czech Academy of Sciences, Žitná 25, Czech Republic;
© Copyright 2012 Elsevier B.V., All rights reserved.

Cited by 25 documents

Bouzebda, S. , Didi, S.
Some asymptotic properties of kernel regression estimators of the mode for stationary and ergodic continuous time processes
(2021) Revista Matematica Complutense
Janák, J.
Parameter Estimation for Stochastic Wave Equation Based on Observation Window
(2021) Acta Applicandae Mathematicae
Rosati, T.C.
Synchronization for KPZ
(2021) Stochastics and Dynamics
View details of all 25 citations
Inform me when this document is cited in Scopus:
Set citation alert Set citation feed
{"topic":{"name":"Fractional Brownian Motion; Rough Paths; Hurst Parameter","id":8382,"uri":"Topic/8382","prominencePercentile":90.06057,"prominencePercentileString":"90.061","overallScholarlyOutput":0},"dig":"39bccd56d44ef0825f30776fca675e27ec9523a992c776ba65f354806e7c8126"}

SciVal Topic Prominence

Topic:
Prominence percentile: