Journal of the Korean Statistical Society

  • 제25권2호
  • /
  • Pages.161-173
  • /
  • 1996
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

Parameter Estimation for an Infinite Dimensional Stochastic Differential Equation

  • 발행 : 1996.06.01
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초록

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

키워드

참고문헌

  1. Technical Report, Center for Stochastic Processes, Dept of Statistics, Univ. of North Carolina v.373 On interacting systems of Hilbert Space valued diffusions A. G. Bhatt;G. Kallianpur;R. L. Karandikar;J. Xiong
  2. Technical Report, Center for Applied Mathematical Sciences, Univ. of Southern California v.93-15 On asymptotic properties of maximum likelihood estimators for parabolic stochastic PDE's M. Hubner;B. L. Rozovskii
  3. Identification of Dynamical Systems with Small Noise Yu, A. Kutoyants
  4. Parameter Estimation for Stochastic processes Yu, A. Kutoyants
  5. Stochastic of Random process v.1;2 R. S. Liptser;A. N. Shiryayev
  6. Stochastic Process. Appl. v.17 Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space valued stochastic differential equations W. Loges
  7. Probability A. N. Shiryayev