• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.707-717
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• 1997

The square of Brownian density process $Q^\lambda$ is defined where $\lambda$ is a parameter. Applying limit theorems of stochastic integrals w.r.t. martingale measure, we prove a weak limit theorem for $Q^\lambda$ in $D_{S'(R^d)}[0,1]$.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.399-409
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• 2009

We study the weak convergence of various models to Fractional Brownian motion. First, we consider arima process and ON/OFF source model which allows for long packet trains and long inter-train distances. Finally, we figure out power spectrum density as a Fourier transform of autocorrelation function of arima model and binary signal model.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.203-210
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• 2015

We consider fractional Brownian motion and FARIMA process with Gaussian innovations and show that the suitably scaled distributions of the FARIMA processes converge to fractional Brownian motion in the sense of finite dimensional distributions. We figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, d, 0) by using R/S method. Finally, we display power spectrum density of FARIMA process.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.267-280
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• 2007

In this paper, we consider the robust estimation for diffusion processes when the sample is observed discretely. As a robust estimator, we consider the minimizing density power divergence estimator (MDPDE) proposed by Basu et al. (1998). It is shown that the MDPDE for diffusion process is weakly consistent. A simulation study demonstrates the robustness of the MDPDE.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.895-906
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• 2015

Diffusion is a mathematical tool to explain the fluctuation of financial assets and the movement of particles in a micro time scale. There are ongoing statistical trials to develop an estimation method for diffusion models based on likelihood. When we estimate diffusion models by applying the maximum likelihood estimation method on data observed at discrete time points, we need to know the transition density of the diffusion. In order to approximate the transition densities of diffusion models, we suggests the method to approximate the path integral of the random process with normal random variables, and compare the numerical properties of the method with other approximation methods.

• Water for future
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• v.27 no.3
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• pp.115-121
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• 1994

Cohesie sediment movement in estuarine systems is strongly affected by the phenomena of aggregation and flocculation. Aggregation is the process where primary particles are clustered together in tightly-packed formations; flocculation is the process where aggregates and single particles are bonded together to form large particle groups of very low specific density. The size, shape and strength of the flocculants control the rate of deposition and the processes of pollutant exchange between suspended sediments and ambient water. In estuarine waters, suspended sediments above the lutocline form the mobile suspension zone while below the lutocline they form the stationary suspension zone. Suspended particles in the mobile zone are generally in a dispersed state and the controlling forces are the Brownian motion and the turbulent flow fluctuations. In the stationary suspension zone, the driving force is the gravity. This paper discusses the settling and particle flocculation characteristics under quiescient flow conditions. Particles are entering the study domain randomly. Particles in the mobile suspension zone are simulated by using the Smoluchowski's model. Flocs created in the mobil suspension zone are moving into the stationary suspension zone where viscosity and drag effects are important. Utilizing the concepts of the maximum Feret's diameter and the Minkowski's sausage logic, the fractal dimension of the flocs within the stationary suspension is estimated and then compared with results obtained by other studies.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2342-2352
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• 1995

Deposition of flame-synthesized silica particles onto a target is utilized in optical fiber preform fabrication processes. The particles are convected and deposited onto the target. Falkner-Skan wedge flow was chosen as the particle laden flow. Typically the particles are polydisperse in size and follow a lognormal size distribution. Brownian diffusion, thermophoresis, and coagulation of the particles were considered and effects of these phenomena on particle deposition were studied. A moment model was developed in order to predict the particle number density and the particle size distribution simultaneously. Particle deposition with various wedge configurations was examined for conditions selected for a typical VAD process. When coagulation was considered, mean particle size and its standard deviation increased and particle number density decreased, compared to the case without coagulation. These results proved the fact that coagulation effect expands particle size distribution. The results were discussed with characteristics of thermal and diffusion boundary layers. As the boundary layers grow in thickness, overall temperature and concentration gradients decrease, resulting in decrease of deposition rate and increase of particle residence time in the flow and thus coagulation effect.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.1
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• pp.61-69
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• 1998

Vapor Axial Deposition (VAD), one of optical fiber preform fabrication processes, is performed by deposition of submicron-size silica particles that are synthesized by combustion of raw chemical materials. In this study, flow field is assumed to be a forced uniform flow perpendicularly impinging on a rotating disk. Similarity solutions obtained in our previous study are utilized to solve the particle transport equation. The particles are approximated to be in a polydisperse state that satisfies a lognormal size distribution. A moment model is used in order to predict distributions of particle number density and size simultaneously. Deposition of the particles on the disk is examined considering convection, Brownian diffusion, thermophoresis, and coagulation with variations of the forced flow velocity and the disk rotating velocity. The deposition rate and the efficiency directly increase as the flow velocity increases, resulting from that the increase of the forced flow velocity causes thinner thermal and diffusion boundary layer thicknesses and thus causes the increase of thermophoretic drift and Brownian diffusion of the particles toward the disk. However, the increase of the disk rotating speed does not result in the direct increase of the deposition rate and the deposition efficiency. Slower flow velocity causes extension of the time scale for coagulation and thus yields larger mean particle size and its geometric standard deviation at the deposition surface. In the case of coagulation starting farther from the deposition surface, coagulation effects increases, resulting in the increase of the particle size and the decrease of the deposition rate at the surface.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.23 no.4
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• pp.416-422
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• 2019

This paper proposes a GPU-based modeling and rendering of 3D clouds using procedural functions. The formation of clouds is based on modified noise function made with fbm(Fractional Brownian Motion). Those noise values turn into densities of droplets of liquid water, which is a critical parameter for forming the three different types of clouds. At the rendering stage, the algorithm applies the ray marching technique to decide the colors of cloud using density values obtained from the noise function. In this process, all lighting attenuation and scattering are calculated by physically based manner. Once we have the clouds, they are blended on the sky, which is also rendered physically. We also make the clouds moving in the sky by the wind force. All algorithms are implemented and tested on GPU using GLSL.