• 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.

• 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.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.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1083-1101
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• 2022

In this paper, we study backward stochastic differential equations (BSDEs shortly) with jumps that have Lipschitz generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. Under just integrability on the data we show that such equations admit a unique solution which belongs to class 𝔻.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.89-100
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• 1996

In this paper we investigate a limit theorem for a non-statioary d-parameter array of associated random variables applying the criterion of the tightness condition in Donsker, M[1951]. Our re-sults imply an extension to the nonstatioary case of Convergence of Probability Measure of billingsley. P[1986]. and analogous results for the d-dimensional associated random measure. These results are also applied to show a new limit theorem for Poisson cluster random mea-sures.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.31-42
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• 1994

In this paper we investigate an functional central limit theorem for a nonstatioary d-parameter array of associated random variables applying the crite-rion of the tightness condition in Bickel and Wichura[1971]. Our results imply an extension to the nonstatioary case of invariance principle of Burton and Kim(1988) and analogous results for the d-dimensional associated random measure. These re-sults are also applied to show a new functional central limit theorem for Poisson cluster random variables.

• Journal of KSNVE
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• v.7 no.3
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• pp.477-488
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• 1997

In order to control vibration in structures, it is desirable to be able to identify dominant paths of vibration transmission from sources through the structure to some points of interest. Structural intensity vector(power flow per width of cross section) using cross spectra is able to measure the vibration power flow at a point in a structure. This paper describes the structural intensity measurement of 2-dimensional structure. Structural intensity of 2-dimensional structure can be obtained from eight point cross spectral measurement per axis, or two point measurement per axis on the assumption of far field. Approximate formulation of the relation between bending waves in structures and structural intensity makes it possible to separate the wave components by which one can get a state of the vibration field. Experimental results are obtained on an infinite plate at the near and far field in flexural vibration. The measurement error of two point measurement is rather bigger than eight point measurement on account of the assumption that Poisson's ratio is 1. The structural intensity vectors on the plate are checked the ability to identify the path of vibration power flow in random excitation and 200Hz sine excitation, the result of two point measurememt is almost the same as the result of eight point measurement in 200Hz sine excitation.