• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.63-68
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• 1990

In this paper, we give the Radon-Nikodym derivative of a measure taking values in a dual Banach space.

• The Mathematical Education
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• v.29 no.2
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• pp.141-143
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• 1990

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• The Pure and Applied Mathematics
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• v.23 no.4
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• pp.339-345
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• 2016

The set of priors in the representation of Choquet expectation is expressed as the one of equivalent martingale measures under some conditions. We show that the set of priors, $\mathcal{Q}_c$ in (1.1) is the same set of $\mathcal{Q}^{\theta}$ in (1.3).

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.161-173
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• 1996

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).

• 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.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.195-205
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• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.