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Spectral asymptotics of some functionals arising in statistical inference for SPDEs

Author

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  • Lototsky, Sergey V.
  • Rosovskii, Boris L.

Abstract

A parameter estimation problem is considered for a stochastic evolution equation on a compact smooth manifold. Specifically, we concentrate on asymptotic properties of spectral estimates, i.e. estimates based on finite number of spatial Fourier coefficients of the solution. Under certain non-degeneracy assumptions the estimate is proved to be consistent, asymptotically normal and asymptotically efficient as the dimension of the projections increases. Unlike previous works on the subject, no commutativity is assumed between the operators in the equation.

Suggested Citation

  • Lototsky, Sergey V. & Rosovskii, Boris L., 1999. "Spectral asymptotics of some functionals arising in statistical inference for SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 69-94, January.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:69-94
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    Cited by:

    1. Cialenco, Igor & Glatt-Holtz, Nathan, 2011. "Parameter estimation for the stochastically perturbed Navier-Stokes equations," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 701-724, April.
    2. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.

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