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Stochastics and DynamicsVolume 9, Issue 2, 2009, Pages 169-185

Asymptotic properties of the maximum likelihood estimator for stochastic parabolic equations with additive fractional brownian motion(Article)(Open Access)

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  • aDepartment of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Str, Chicago, IL 60616, United States
  • bDepartment of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, CA 90089, United States
  • cDepartment of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic

Abstract

A parameter estimation problem is considered for a diagonalizable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter H ≥ 1/2. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier coefficients increases. A necessary and sufficient condition for consistency and asymptotic normality is presented in terms of the eigenvalues of the operators in the equation. © 2009 World Scientific Publishing Company.

Author keywords

Asymptotic normalityErgodicityParameter estimationStochastic evolution equations

Funding details

Funding sponsor Funding number Acronym
MSM 4977751301
National Science Foundation
See opportunities by NSF		DMS-0237724NSF
Scuola Normale SuperioreSNS

  • 1

    S. V. L. acknowledges support from the NSF CAREER award DMS-0237724, as well as hospitality and support of the Scuola Normale Superiore (Pisa, Italy). SVL and JP are grateful to the Institut Mittag-Leffler (Djursholm, Sweden) for the hospitality and support. The work of JP was also partially supported by MSMT Research Plan MSM 4977751301. The authors are grateful to Bohdan Maslowski and the anonymous referee for very helpful suggestions.

  • ISSN: 02194937
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1142/S0219493709002610
  • Document Type: Article

  Cialenco, I.; Department of Applied Mathematics, Illinois Institute of Technology, 10 West 32nd Str, United States;
© Copyright 2009 Elsevier B.V., All rights reserved.

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