• 응용통계연구
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• 제23권2호
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• pp.383-392
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• 2010

확산모형은 최근 금융현상의 연구 등에 자주 사용되는 모형이다. 본 연구에서는 확산모형의 추정에서 중요한 역할을 하는 전이확률밀도를 구하는 방법과 이를 급수전개 방식으로 근사하는 기존 연구들을 검토하여 보고, 급수전개법에서의 계수를 손쉽게 구할 수 있는 방법을 고려하게 된다. 급수전개법 계산과정에서 중요한 허밋다항식에 딘킨연산자를 반복적으로 적용하는 과정을 손쉽게 계산할 수 있는 알고리즘을 제안한다.

• 대한수학회지
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• 제32권2호
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• pp.211-236
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• 1995

The purpose of this paper is to provide a transient diffusion approximation of queue size distribution for M/G/m/N system. The M/G/m/N system can be expressed as follows. The interarrival times of customers are exponential and the service times of customers have general distribution. The system can hold at most a total of N customers (including the customers in service) and any further arriving customers will be refused entry to the system and will depart immediately without service. The queueing system with finite capacity is more practical model than queueing system with infinite capacity. For example, in the design of a computer system one of the important problems is how much capacity is required for a buffer memory. It its capacity is too little, then overflow of customers (jobs) occurs frequently in heavy traffic and the performance of system deteriorates rapidly. On the other hand, if its capacity is too large, then most buffer memories remain unused.

• 한국경영과학회지
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• 제34권4호
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• pp.15-26
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• 2009

Bass diffusion model have played a central role in studying the diffusion of the new products since 1969, the year of publication of Bass model. Almost 750 publications based on the Bass diffusion model have explored extensions and applications. Extension models can be divided into two types. One is the model containing marketing-mix variables and the other is the model containing additional parameters. This paper presents another extension model of the latter type. Our model allows the time varying coefficients of innovation and imitation. Two pieces approximation of time varying coefficients is introduced and it's parameters are estimated based on NLS(Non-Linear Mean Square) method. Empirical studies are performed and the results show that our model is superior to the basic Bass model and the NUI(Non-Uniform Influence) model which is the well-known extension of the Bass model. The model developed in this paper is, also, transformed into the Bass model with the ready potential adopters in order to enhance the descriptive power.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2001년도 춘계학술대회 논문집 유기절연재료 전자세라믹 방전플라즈마 연구회
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• pp.164-167
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• 2001

The electron transport coefficients, the electron drift velocity W, the longitudinal diffusion coefficient $ND_L$ and $D_L/{\mu}$, in pure $CO_2$ were calculated over the wide E/N range from 0.01 to 500 Td at 1 Torr by two-term approximation of the Boltzmann equation for determination of electron collision cross sections set and for quantitative characteristic analysis of $CO_2$ molecular gas. And for propriety of two-term approximation of Boltzmann equation analysis, the calculated results compared with the electron transport coefficients measured by Nakamura.

• Bulletin of the Korean Chemical Society
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• 제32권4호
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• pp.1336-1340
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• 2011

Molecular dynamics simulations have been performed to investigate the transport properties of self-diffusion coefficients in the penetrable-sphere model system. The resulting simulation data for the product of the packing fraction and the self-diffusion coefficient exhibit a transition from an increasing function of density in lower repulsive systems, where the soft-type collisions are dominant, to a decreasing function in higher repulsive systems, where most particle collisions are the hard-type reflections due to the low-penetrability effects. A modified Enskog-like equation implemented by the effective packing fraction with the mean-field energy correction is also proposed, and this heuristic approximation yields a reasonably good result even in systems of high densities and high repulsive energy barriers.

• 한국경영과학회지
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• 제38권1호
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• pp.201-216
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• 2013

Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

• 응용통계연구
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• 제28권5호
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• pp.895-906
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• 2015

확산모형은 입자의 운동현상과 금융자산의 미시적 가격변동을 설명하기 위하여 사용되는 수리적 모형이다. 확산모형의 추정방법에 관한 논의는 다양한 분야에서 이루어져 왔다. 통계학적 관점에서 우도적 방법에 기반한 확산모형의 추정방법을 개발하려는 시도가 계속되어 왔다. 이산시간 간격으로 관측된 자료를 이용하여 확산모형을 추정할 때 최대우도 추정법을 적용하기 위해서는 확산모형에 대한 전이확률 밀도함수를 구해야 한다. 본 연구에서는 확산모형의 전이확률밀도를 근사하기 위하여, 정규분포를 따르는 확률변수를 이용하여 브라운다리 확률과정에 대한 경로적분을 대체하는 방법을 제안하고, 그 수치적 성질을 다른 방법들과 비교한다.

• 대한수학회보
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• 제35권4호
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• pp.837-845
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• 1998

In this work, we consider Euler approxiamtion for one-dimensional jump-diffusion processes under Yamada-Watanabe type conditions on the coefficients which turns out to converge to the strong solution in uniform $L^1$-sense.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.599-609
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• 2014

We refer to the saturation assumptions on the finite element approximation for a one dimensional convection-diffusion model. By examining piecewise linear finite elements with refined mesh by half and hierarchical bases, we verify the saturation results, respectively.

• 한국에너지공학회:학술대회논문집
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• 한국에너지공학회 1993년도 추계학술발표회 초록집
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• pp.99-102
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• 1993

A consistent general order nodal method for solving the three-dimensional neutron diffusion equation in (x-y-z) geometry has been derived by using a weighted integral technique and expanding the spatial variable by the Legendre orthogonal series function. The equation set derived can be converted into any order nodal schemes. It forms a compact system for general order of nodal moments. The method utilizes fewer unknown variables in the schemes for iterative-convergence solution than other nodal methods listed in the literatures, and because the method utilizes the analytic solutions of the transverse-integrated one dimensional equations and a consistent approximation for a given spatial variable through all the solution procedures, which renders the use of an approximation for the transverse leakages no longer necessary, we can expect extremely accurate solutions and the solution would converge exactly when the mesh width is decreased or the approximation order is increased.