• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.329-342
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• 2002

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.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.75-88
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• 1997

In this paper, a two-parameter version of Ikeda-Watanabe's mollifiers approximation of the Brownian motion is considered, and an approximation theorem corresponding to the one parameter case is proved. Using this approximation, we formulate Wong-Zakai type theorem is a Stochastic Differential Equation (SDE) driven by a two-parameter Wiener process.

• The KIPS Transactions:PartB
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• v.11B no.3
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• pp.297-302
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• 2004

In this paper, the 3-D shape description for the objects with the cone ridge and valley surfaces, and the corresponding threshold value selection for surface classification are considered. The existing method based on the mean and Gaussian curvatures(H and K) of differential geometries cannot properly describe cone primitives, which are some of the most common objects in the real world. Also the existing method for surface classification based on the sign values of H and K has Problems in practical applications. For this, cone surface shapes are classified cone ridges and cone valleys are derived from surfaces using the fact that H values are constant case of cylinder surfaces and variable for cone surfaces, respectively. Also threshold value selection for surface classification from a statistical point of view is proposed. The effectiveness of the proposed methods are verified through experiments.