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Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

Applied Mathematics and Optimization volume 57, pages 401–429 (2008)Cite this article

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.

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Author information

Affiliations

  1. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czech Republic

    Bohdan Maslowski

  2. Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Univerzitní 22, 306 14, Plzeň, Czech Republic

    Jan Pospíšil

Authors
  1. Bohdan Maslowski
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  2. Jan Pospíšil
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Corresponding author

Correspondence to Bohdan Maslowski.

Additional information

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

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Maslowski, B., Pospíšil, J. Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process. Appl Math Optim 57, 401–429 (2008). https://doi.org/10.1007/s00245-007-9028-3

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Keywords

  • Stochastic partial differential equations
  • Fractional Brownian motion
  • Fractional Ornstein-Uhlenbeck process
  • Strictly stationary solution
  • Ergodicity
  • Parameter estimates