• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.967-990
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• 2006

In this paper, we evaluate first variations, conditional first variations and conditional Fourier-Feynman transforms of cylinder type functions over Wiener paths in abstract Wiener space and then, investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transform of those functions. Finally, we derive the conditional Fourier-Feynman transform for the product of cylinder type function which defines the functions in a Banach algebra introduced by Yoo, with n linear factors.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1031-1056
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• 2005

In this paper, we define the conditional first variation over Wiener paths in abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with n linear factors.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.57-69
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• 2014

We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1561-1577
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• 2014

In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.573-586
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• 2016

We study the conditional integral transforms and conditional convolutions of functionals defined on K[0, T]. We consider a general vector-valued conditioning functions $X_k(x)=({\gamma}_1(x),{\ldots},{\gamma}_k(x))$ where ${\gamma}_j(x)$ are Gaussian random variables on the Wiener space which need not depend upon the values of x at only finitely many points in (0, T]. We then obtain several relationships and formulas for the conditioning functions that exist among conditional integral transform, conditional convolution and first variation of functionals in $E_{\sigma}$.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.1-18
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• 2012

We study various relationships that exist among generalized conditional integral transform, generalized conditional convolution and generalized first variation for a class of functionals defined on K[0, T], the space of complex-valued continuous functions on [0, T] which vanish at zero.

• Asia-Pacific Journal of Business
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• v.11 no.3
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• pp.199-215
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• 2020

Purpose - This article tries to test if the conditional consumption capital asset pricing model (CCAPM) with bank credit for household as a conditional variable can explain the cross-sectional variation of stock returns in Korea. The performance of conditional CCAPM is compared to that of multifactor asset pricing models based on Arbitrage Pricing Theory. Design/methodology/approach - This paper extends the simple CCAPM to the conditional version of CCAPM by using bank credit for household as conditioning information. By employing KOSPI and KOSDAQ stocks as test assets from the second quarter of 2003 to the first quarter of 2018, this paper estimates risk premiums of conditional CCAPM and a variety of multifactor linear models such as Fama-French three and five-factor models. The significance of risk factors and the adjusted coefficient of determination are the basis for the comparison in models' performances. Findings - First, the paper finds that conditional CCAPM with bank credit performs as well as the multifactor linear models from Arbitrage Pricing theory on 25 test assets sorted by size and book-to-market. When using long-term consumption growth, the conditional CCAPM explains the cross-sectional variation of stock returns far better than multifactor models. Not only that, although the performances of multifactor models decrease on 75 test assets, conditional CCAPM's performance is well maintained. Research implications or Originality - This paper proposes bank credit for household as a conditional variable for CCAPM. This enables CCAPM, one of the most famous economic asset pricing models, to conform with the empirical data. In light of this, we can now explain the cross-sectional variation of stock returns from an economic perspective: Asset's riskiness is determined by its correlation with consumption growth conditional on bank credit for household.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.395-404
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• 2012

Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.65-65
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• 2002

In remote sensing, images are acquired over the same area by sensors of different spectral ranges (from the visible to the microwave) and/or with different number, position, and width of spectral bands. These images are generally partially redundant, as they represent the same scene, and partially complementary. For many applications of image classification, the information provided by a single sensor is often incomplete or imprecise resulting in misclassification. Fusion with redundant data can draw more consistent inferences for the interpretation of the scene, and can then improve classification accuracy. The common approach to the classification of multisensor data as a data fusion scheme at pixel level is to concatenate the data into one vector as if they were measurements from a single sensor. The multiband data acquired by a single multispectral sensor or by two or more different sensors are not completely independent, and a certain degree of informative overlap may exist between the observation spaces of the different bands. This dependence may make the data less informative and should be properly modeled in the analysis so that its effect can be eliminated. For modeling and eliminating the effect of such dependence, this study employs a strategy using self and conditional information variation measures. The self information variation reflects the self certainty of the individual bands, while the conditional information variation reflects the degree of dependence of the different bands. One data set might be very less reliable than others in the analysis and even exacerbate the classification results. The unreliable data set should be excluded in the analysis. To account for this, the self information variation is utilized to measure the degrees of reliability. The team of positively dependent bands can gather more information jointly than the team of independent ones. But, when bands are negatively dependent, the combined analysis of these bands may give worse information. Using the conditional information variation measure, the multiband data are split into two or more subsets according the dependence between the bands. Each subsets are classified separately, and a data fusion scheme at decision level is applied to integrate the individual classification results. In this study. a two-level algorithm using hierarchical clustering procedure is used for unsupervised image classification. Hierarchical clustering algorithm is based on similarity measures between all pairs of candidates being considered for merging. In the first level, the image is partitioned as any number of regions which are sets of spatially contiguous pixels so that no union of adjacent regions is statistically uniform. The regions resulted from the low level are clustered into a parsimonious number of groups according to their statistical characteristics. The algorithm has been applied to satellite multispectral data and airbone SAR data.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2003.11a
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• pp.3-8
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• 2003

Census data are usually provided at an aggregated level. However, the aggregated data are essentially arbitrary geographical areas. The areal units used to report census data have no natural or meaningful geographical identity. Unfortunately, this means that analyses of these area aggregations may be conditional upon the set of zones, which are presented. This effect is known as the modifiable areal unit problem (MAUP) and has two related aspects. First, scale effect is the variation in numerical results that occurs due to the number of zones used in an analysis. Second, results may also differ between different ways of aggregating exactly the same data to the same scale; this may be called the aggregation effect (Openshaw, 1984). This study aims to provide a practical tool for the study of MAUP. I have created a set of 91 areal units based on 280 basic units in Nonhyun-2 dong to solve zoning problem and scale problem. We can easily recognize the importance of areal classification as statistics were different according to areal classification.