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Parameter Estimation for a Hilbert Space-valued Stochastic Differential Equation ？ $\pm$

Kim, Yoon-Tae (Department of Statistics, Hallym University)
Park, Hyun-Suk (Department of Statistics, Hallym University)

Publication Information

Journal of the Korean Statistical Society / v.31, no.3, 2002 , pp. 329-342 More about this Journal

Abstract

We deal with asymptotic properties of Maximum Likelihood Estimator(MLE) for the parameters appearing in a Hilbert space-valued Stochastic Differential Equation(SDE) and a Stochastic Partial Differential Equation(SPDE). In paractice, the available data are only the finite dimensional projections to the solution of the equation. Using these data we obtain MLE and consider the asymptotic properties as the dimension of projections increases. In particular we explore a relationship between the conditions for the solution and asymptotic properties of MLE.

Keywords

Stochastic differential equation; maximum likelihood estimator; Radon-Nikodym derivative; statistical differential geometry;

Citations & Related Records

Reference

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