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On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's
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  • Published: June 1995

On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's

  • M. Huebner1 &
  • B. L. Rozovskii2 

Probability Theory and Related Fields volume 103, pages 143–163 (1995)Cite this article

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Summary

We investigate asymptotic properties of the maximum likelihood estimators for parameters occurring in parabolic SPDEs of the form

$$du(t,x) = (A_0 + \theta A_1 )u(t,x)dt + dW(t,x),$$

whereA 0 andA 1 are partial differential operators andW is a cylindrical Brownian motion. We introduce a spectral method for computing MLEs based on finite dimensional approximations to solutions of such systems, and establish criteria for consistency, asymptotic normality and asymptotic efficiency as the dimension of the approximation goes to infinity. We derive the asymptotic properties of the MLE from a condition on the order of the operators. In particular, the MLE is consistent if and only if ord(A 1)≧1/2(ord(A 0+θA 1)−d).

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Author information

Authors and Affiliations

  1. Department of Statistics and Probability, Michigan State University, 48824, East Lansing, MI, USA

    M. Huebner

  2. Center for Applied Mathematical Sciences, University of Southern California, 90089-1113, Los Angeles, CA, USA

    B. L. Rozovskii

Authors
  1. M. Huebner
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  2. B. L. Rozovskii
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Additional information

This work was partially supported by ONR Grant # N00014-91-J-1526 and NSF Grant # DMS-9002997

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Huebner, M., Rozovskii, B.L. On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's. Probab. Th. Rel. Fields 103, 143–163 (1995). https://doi.org/10.1007/BF01204212

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  • Received: 17 August 1993

  • Revised: 06 February 1995

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01204212

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Mathematics Subject Classification

  • 60H
  • 62F
  • 65U
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