• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.683-693
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• 2008

In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Transactions of Materials Processing
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• v.5 no.1
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• pp.37-46
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• 1996

Superplastic forming/diffusion bonding (SPF/DB) processes were analyzed using a rigid visco-plastic finite element method. The optimum pressure-time relationship for a target strain rate and thickness distributions were predicted by two-node line elements based on the membrane approximation for plane strain. Material behavior during SPF/DB of the integral structures having complicated shapes was investigated. The tying condition is employed for the analysis of inter-sheet contact problems. A movement of rib structure is successfully predicted during the forming.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.367-376
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• 2010

Recently various methods were suggested and reviewed for estimating diffusion processes. Out of suggested estimation method, we mainly concerns on the estimation method using saddlepoint approximation method, and we suggest a term saddlepoint approximation(ASP) method which is the simplest saddlepoint approximation method. We will show that ASP method provides fast estimator as much as Euler approximation method(EAM) in computing, and the estimator also has good statistical properties comparable to the maximum likelihood estimator(MLE). By simulation study we compare the properties of ASP estimator with MLE and EAM, for Ornstein-Uhlenbeck diffusion processes.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.599-609
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• 2010

Many of financial data are explained via diffusion models in modern financial research. Various types of estimation methods of diffusion processes were suggested by many authors. In this paper, we tested the properties of the NLL estimation method, suggested by Shoji and Ozaki (1998), of diffusion processes in the view of the bias and variance of the estimators and applied the method to estimate the model parameters for the U.S. fedral funds rate data and Korean inter-bank exchange rate data. By simulation study we showed that the NLL method provides relatively good estimators, in the meaning that the estimator has less bias than the Euler method, while keeping the variance similar level. We also provide the NLL estimates of U.S fedral funds rate data and Korean inter-bank exchange rate data.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.455-460
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• 2007

In allelic model $X=(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)=f(p(t))-{\int}_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator $L^*$. Since the martingale problem for this operator $L^*$ is related to diffusion processes, we can define a integral which is combined with operator $L^*$ and a bilinar form $<{\cdot},{\cdot}>$. We can find properties for this integral using maximum principle.

• Journal of the Korean institute of surface engineering
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• v.49 no.1
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• pp.104-109
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• 2016

Graphite's thermal stability facilitates its widespread use as crucibles and molds in high temperatures processes. However, carbon atoms can be rather easily detached from pores and outer surfaces of the graphite due to the weak molecular force of the c axis of graphites. Detached carbon atoms are known to become a source of dust during fabrication processes, eventually lowering the effective yield of products. As an effort to reduce these problems of dust scattering, we have fabricated SiC composites by employing Si vapor infiltration method into the pores of graphites. In order to understand the diffusion process of the Si vapor infiltration, Si and C atomic percentages of fabricated SiC composites are carefully measured and the diffusion law is used to estimate the diffusion coefficient of Si vapor. A quadratic equation is obtained from the experimental results using the least square method. Diffusion coefficient of Si vapor is estimated using this quadratic equation. The result shows that the diffusion length obtained through the Si vapor infiltration method is about 10.7 times longer than that obtained using liquid Si and clearly demonstrates the usefulness of the present method.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.147-158
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• 2011

In this paper, we consider a multi-dimensional diffusion process in a self-similar random environment and prove a limit theorem for the shape of the full trajectory of the diffusion by using the localization phenomenon.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.801-811
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• 2008

Modeling financial phenomena with diffusion processes is a commonly used methodology in the area of modern finance. Recently, various types of diffusion models have been suggested to explain the specific financial processes, and their related inference methodology have been also developed. In particular, likelihood methods for the efficient and accurate inference have been explored in various ways. In this paper, we review the mathematical properties of an approximated likelihood method, which is obtained by linearizing the drift coefficient of a diffusion process.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.695-709
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• 2013

Calcium is well known role for signal transduction in a neuron cell. Various processes and parameters modulate the intracellular calcium signaling process. A number of experimental and theoretical attempts are reported in the literature for study of calcium signaling in neuron cells. But still the role of various processes, components and parameters involved in calcium signaling is still not well understood. In this paper an attempt has been made to develop two dimensional finite element model to study calcium diffusion in neuron cells. The JRyR, JSERCA and JLeak, the exogenous buffers like EGTA and BAPTA, and diffusion coefficients have been incorporated in the model. Appropriate boundary conditions have been framed. Triangular ring elements have been employed to discretized the region. The effect of these parameters on calcium diffusion has been studied with the help of numerical results.