• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.229-236
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• 2011

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

• 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.

• The Korean Journal of Financial Management
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• v.24 no.4
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• pp.1-43
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• 2007

The traditional Black-Scholes model for option pricing is based on the assumption that the log-return of the underlying asset follows a Brownian motion. But this assumption has been criticized for being unrealistic. Thus, for the last 20 years, many attempts have been made to adopt different stochastic processes to derive new option pricing models. The option pricing models based on L$\acute{e}$vy processes are being actively studied originating from the Gerber-Shiu model driven by H. U. Gerber and E. S. W. Shiu in 1994. In 2004, G. H. L. Cheang derived an option pricing model under multiple L$\acute{e}$vy processes, enabling us to adopt drift and jumps to the Gerber-Shiu model, while Gerber and Shiu derived their model under one L$\acute{e}$vy process. We derive the Gerber-Shiu model which includes drift and jumps under L$\acute{e}$vy processes. By adopting a Gamma distribution, we expand the Heston model which was driven in 1993 to include jumps. Then, using KOSPI200 index option data, we analyze the price-fitting performance of our model compared to that of the Black-Scholes model. It shows that our model shows a better price-fitting performance.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.801-810
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• 2018

Diffusion is a random process used to model financial and physical phenomena. When we construct statistical models for repeatedly observed diffusion processes, the idea of random effects needs to be considered. In this research, we introduce random parameters for an Ornstein-Uhlenbeck diffusion model and geometric Brownian motion diffusion model. In order to apply the maximum likelihood estimation method, we tried to build likelihoods in closed-forms, by assuming appropriate distributions for random effects. We applied the random effect models to data consisting of Dow Jones Industrial Average indices recorded daily over 27 years from 1991 to 2017.

• Communications for Statistical Applications and Methods
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• v.22 no.3
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• pp.277-283
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• 2015

Pickands constant $H_{\alpha}$ appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of $H_{\alpha}$ is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of $H_{\alpha}$. In this paper, we attempt to compute numerically $H_{\alpha}$ based on its representation derived by $H{\ddot{u}}sler$ (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture $H_{\alpha}=1/{\Gamma}(1/{\alpha})$ for 0 < ${\alpha}$ ${\leq}$ 2. This conjecture does not seem compatible with our simulation result for 1 < ${\alpha}$ < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1105-1119
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• 2010

We consider jump processes which has only downward jumps with size a fixed fraction of the current process. The jumps of the pro cesses are interpreted as crashes and we assume that the jump intensity is a nondecreasing function of the current process say $\lambda$(X) (X = X(t) process). For the case of $\lambda$(X) = $X^{\alpha}$, $\alpha$ > 0, we show that the process X shold explode in finite time, say $t_e$, conditional on no crash For the case of $\lambda$(X) = (lnX)$^{\alpha}$, we show that $\alpha$ = 1 is the borderline of two different classes of processes. We generalize the model by adding a Brownian noise and examine the blow up properties of the sample paths.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1999.06a
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• pp.115-127
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• 1999

The charged clusters or particles, which contain hundreds to thousands of atoms or even more, are suggested to form in the gas phase in the thin film processes such as CVD, thermal evaporation, laser ablation, and flame deposition. All of these processes are also used in the gas phase synthesis of the nanoparticles. Ion-induced or photo-induced nucleation is the main mechanism for the formation of these nanoclusters or nanoparticles inthe gas phase. Charged clusters can make a dense film because of its self-organizing characteristics while neutral ones make a porous skeletal structure because of its Brownian coagulation. The charged cluster model can successfully explain the unusual phenomenon of simultaneous deposition and etching taking place in diamond and silicon CVD processes. It also provides a new interpretation on the selective deposition on a conducting material in the CVDd process. The epitaxial sticking of the charged clusters on the growing surface is gettign difficult as the cluster size increases, resulting in the nanostructure such as cauliflowr or granular structures.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.9 no.3
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• pp.289-294
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• 1999

The charged clusters or particles, which contain hundreds to thousands of atoms or even more, are suggested to from in the gas phase in the thin film processes such as CVD, thermal evaporation, laser ablation, and flame deposition. All of these processes are also phase synthesis of the nanoparticels. Ion-induced or photo-induced nucleation is the main mechanism for the formation of these nanoclusters or nanoparticles in the gas phase. Charge clusters can make a dense film because of its self-organizing characteristics while neutral ones make a porous skeletal structure because of its Brownian coagulation. The charged cluster model can successfully explain the unusual phenomenon of simultaneous deposition and etching taking place in diamond and silicon CVD processes. It also provides a new interpretation on the selective deposition on a conducting material in the CVD process. The epitaxial sticking of the charged clusters on the growing surface is getting difficult as the cluster size increases, resulting in the nanostructure such as cauliflower or granular structures.

• 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 Korean Data and Information Science Society
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• v.21 no.1
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• pp.179-183
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• 2010

In this paper, we consider the change point problem in diusion processes based on discretely observed sample. Particularly, we consider the change point test for the dispersion parameter when the drift has unknown parameters. In performing a test, we employ the cusum of squares test based on the residuals. It is shown that the test has a limiting distribution of the sup of a Brownian bridge. A simulation result as to the Ornstein-Uhlenbeck process is provided for illustration. It demonstrates the validity of our test.