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Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations

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  • Loges, Wilfried

Abstract

We prove Girsanov-type theorems for Hilbert space-valued stochastic differential equations and apply them to a parameter estimation problem for linear infinite dimensional stochastic differential equations. In particular we construct the asymptotic statistical theory of the estimator, proving strong consistency and asymptotic normality.

Suggested Citation

  • Loges, Wilfried, 1984. "Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 243-263, July.
    • Handle: RePEc:eee:spapps:v:17:y:1984:i:2:p:243-263
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    Cited by:

    1. Kazimierczyk, Piotr, 1992. "Explicit correction formulae for parametric identification of stochastic differential systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 433-450.
    2. M. Huebner, 1999. "Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic PDEs Disturbed by Small Noise," Statistical Inference for Stochastic Processes, Springer, vol. 2(1), pages 57-68, January.
    3. Kim, Yoon Tae, 1999. "Parameter estimation in infinite-dimensional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 195-204, November.
    4. 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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