• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.335-354
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• 2007

In this paper, we define an analogue of generalized Wiener measure and investigate its basic properties. We define (${\hat}It{o}$ type) stochastic integrals with respect to the generalized Wiener process and prove the ${\hat}It{o}$ formula. The existence and uniqueness of the solution of stochastic differential equation associated with the generalized Wiener process is proved. Finally, we generalize the linear filtering theory of Kalman-Bucy to the case of a generalized Wiener process.

• Journal of the Korea Society of Computer and Information
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• v.18 no.3
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• pp.91-96
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• 2013

Because the r-fold Wiener process is truly infinitely dimensional and a computer can only handle finitely dimensional subspaces, we study in this paper the basic properties of the m-dimensional approximation function of the r-fold Wiener process.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.751-762
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• 2020

We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.

• Korean Chemical Engineering Research
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• v.61 no.1
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• pp.89-96
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• 2023

The Wiener-type nonlinear model where a static nonlinear block follows a dynamic linear block is widely used to describe the dynamics of chemical processes. A long process excitation step is typically needed to identify this Wiener-type nonlinear model with two blocks. In order to cope with this disadvantage, an identification method for the Wiener-type nonlinear model that uses only a single-step response is proposed here. The proposed method estimates the response of the dynamic linear sub-block from the initial part of the step response, and then the static nonlinear sub-block is identified. Because the only single-step response is used to identify the Wiener-type nonlinear model, there is great benefit in time and cost for obtaining process response. The performance of the proposed identification method with the single-step response is verified through a representative Wiener-type nonlinear process, a pH titration process, and a liquid level system.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.691-701
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• 2012

In this note, we define the It$\hat{o}$ integral with respect to analogue of Wiener process and investigate its various properties and examples.

• Proceedings of the Acoustical Society of Korea Conference
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• 1992.06a
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• pp.33-36
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• 1992

In this paper we propose the impulse noise-robust Wiener filter based on a combination of Wiener and modified trimmed mean(MTM) filters. The robust Wiener filter uses the trimming operation of the MTM filter to replace the outliers with the median within the window and the new set of samples which can be considered as the random process with same mean are inputted into the following Wiener filter. We show that the robust Wiener filter is effective in frequency selective filtering of nonstationary signals while preserving signal edges with the rejection of impulse noise.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9C
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• pp.743-748
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• 2008

This paper makes a research on the equivalent Wiener-Hopf equation which can obtain the coefficient of TDL filter on orthogonal input signal in terms of mean square error. Using this result, we can present the coefficient and error of TDL filter directly without inverse orthogonalization process on orthogonal input signal. We make a theoretical analysis on MMSE and show an Wiener-Hopf solution and the proposed equivalent one in mathematical example simultaneously.

• 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.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.379-390
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• 2000

In this paper the limit theorems on lag increments of a Wiener process due to Chen, Kong and Lin [1] are developed to the case of a Gaussian process via estimating upper bounds of large deviation probabilities on suprema of the Gaussian process.