• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1049-1061
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• 2017

The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.127-137
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• 1992

In this paper we investigate scaling limits for associated random measures satisfying some moment conditions. No stationarity is required. Our results imply an improvement of a central limit theorem of Cox and Grimmett to associated random measure and an extension to the nonstationary case of scaling limits of Burton and Waymire. Also we prove an invariance principle for associated random measures which is an extension of the Birkel's invariance principle for associated process.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.19-27
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• 2001

In this paper we study another kind of the large deviation property, i.e. moderate deviation type for random amount of random measures on $R^d$ about a Poisson point process and a Poisson center cluster random measure.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.105-112
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• 1996

Softwares including random number generation are abundant in modern informative society. But it's hard to get directly multivariate multinomial random numbers from existing softwares. Multivariate multinomial random numbers are greatly used in social and medical sciences. In this paper, we show that desired multivariate multinomial random numbers can be easily generated by the aids of existing random number generating software. Some characteristics of multivariate multinomial distribution are surveyd. Measures of association for the generated random numbers were computed and compared with population ones via simulation study.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.269-289
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• 2005

An infinite system of stochastic differential equations (SDE)driven by Brownian motions and compensated Poisson random measures for the locations and weights of a collection of particles is considered. This is an analogue of the work by Kurtz and Xiong where compensated Poisson random measures are replaced by white noise. The particles interact through their weighted measure V, which is shown to be a solution of a stochastic differential equation. Also a limit theorem for system of SDE is proved when the corresponding Poisson random measures in SDE converge to white noise.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.26 no.11
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• pp.999-1011
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• 2015

In modern electronic warfare, RADAR is under constant threat of ECM(Electronic Counter Measures) signals from nearby jammers. The conventional linear frequency modulated(Linear-FM) waveform is easy to be intercepted to estimate its signal parameters due to its periodical phase transition. Recently, APCN(Advanced Pulse Compression Noise) waveform using random amplitude and phase transition was proposed for LPI(Low probability of Intercept). But random phase code signals such as APCN waveform tend to be sensitive to Doppler frequency shift and result in performance degradation during moving target detection. In this paper, random phase and code rate transition based radar waveform(RPCR) is proposed for Doppler tolerance improvement. Time frequency analysis is carried out through ambiguity analysis to validate the improved Doppler tolerance of RPCR waveform. As a means to measure the vulnerability of the proposed RPCR waveform against LPI, WHT(Wigner-Hough Transform) is adopted to analyze and estimate signal parameters for ECCM(Electronic Counter Counter Measures) application.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.411-418
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• 1997

In this note we prove a functional central limit theorem for nonstationary linearly positive quadrant dependent random fields. We extend it to the case of random measures.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.394-397
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• 2004

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.265-272
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• 1996

In this note we prove a functional central limit theorem for linearly positive quadrant dependent(LPQD) random fields, satisfying some assumption on covariances and the moment condition $\sup_{n \in \Zeta^d} E$\mid$S_n$\mid$^{2+\rho} < \infty$ for some $\rho > 0$. We also apply this notion to random measures.