• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.265-274
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• 2016

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.991-1017
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• 2016

In this paper we define a generalized analytic Fourier-Feynman transform associated with Gaussian process on the function space $C_{a,b}[0,T]$. We establish the existence of the generalized analytic Fourier-Feynman transform for certain bounded functionals on $C_{a,b}[0,T]$. We then proceed to establish a translation theorem for the generalized transform associated with Gaussian process.

• Bulletin of the Korean Chemical Society
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• v.19 no.10
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• pp.1068-1072
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• 1998

We present results of molecular dynamic (MD) simulations for the segmental motion of liquid n-butane as the base case for a consistent study for conformational transition from one rotational isomeric state to another in long chains of liquid n-alkanes. The behavior of the hazard plots for n-butane obtained from our MD simulations are compared with that for n-butane of Brownian dynamics study. The MD results for the conformational transition of n-butane by a Poisson process form the total first passage times are different from those from the separate t-g and g-t first passage times. This poor agreement is probably due to the failure of the detailed balance between the fractions of trans and gauche. The enhancement of the transitions t-g and g-t at short time regions are also discussed.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.141-147
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• 1995

A diffusion model for a system subject to random shocks is introduced. It is assumed that the state of system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. It is also assumed that the shocks coming to the system according to a Poisson process decrease the state of the system by a random amount. It is further assumed that a repairman arrives according to another Poisson process and repairs or replaces the system i the system, when he arrives, is in state zero. A forward differential equation is obtained for the distribution function of X(t), the state of the systme at time t, some boundary conditions are discussed, and several interesting characteristics are derived, such as the first passage time to state zero, F(0,t), the probability of the system being in state zero at time t, and F(0), the limit of F(0,t) as t tends to infinity.

• 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.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.529-552
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• 2014

As we know, some indices and data are strong influence to the price movement of some assets now, but not to another assets and in future. Thus we define some asset models for several time intervals; intraday, weekly, monthly, and yearly asset models. We define these asset models by using Brownian motion with volatility and Poisson process, and several deterministic functions(index function, twitter data function and big-jump simple function etc). In our asset models, these deterministic functions are the positive or negative levels of auxiliary indices, of analyzed data, and for imminent and extreme state(for example, financial shock or the highest popularity in the market). These functions determined by indices, twitter data and shocking news are a kind of one of speciality of our asset models. For reasonableness of our asset models, we introduce several real data, figurers and tables, and simulations. Perhaps from our asset models, for short-term or long-term investment, we can classify and reference many kinds of usual auxiliary indices, information and data.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.655-663
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• 2003

The fundamental tenn structure model is based on the modelling of the short rate. It is well-known that the short rate depends on the interest rate policy of monetary authorities, especially on the official rate. Babbs and Webber(1994) modelled the tenn structure of interest rates using the official rate. They assume that the official rate follows a jump process. This reflects that the official rate infrequently changes. In this paper, we test this official tenn structure model and compare the jump-diffusion model with the pure diffusion model.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.1344-1346
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• 1996

In this paper, we discuss an informal analysis of diffusion, global optimization properties of Langevine competitive learning neural network. In the view of the stochastic process, it is important that competitive learning gurantee an optimal solution for pattern recognition. We show that the binary reinforcement function in Langevine competitive learning is a brownian motion as Gaussian process, and construct the Fokker-Plank equation for the proposed neural network. Finally, we show that the informal analysis of the proposed algorithm has a possiblity of globally optimal. solution with the proper initial condition.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.227-237
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• 2002

A numerical technique for simulating the aggregation of charged particles was presented with a Brownian dynamic simulation in the free molecular regime. The Langevin equation was used for tracking each particle making up an aggregate. A periodic boundary condition was used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered the thermal force and the electrostatic force for the calculation of the particle motion. The electrostatic force on a particle in the simulation cell was considered as a sum of electrostatic forces from other particles in the original cell and its replicate cells. We assumed that the electric charges accumulated on an aggregate were located on its center of mass, and aggregates were only charged with pre-charged primary particles. The morphological shape of aggregates was described in terms of the fractal dimension. In the simulation, the fractal dimension for the uncharged aggregate was D$\_$f/ = 1.761. The fractal dimension changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states. In the bipolar charge state, the average sizes of aggregates were larger than that of the uncharged state in the early and middle stages of aggregation process, but were almost the same as the case of the uncharged state in the final stage. On the other hand, in the unipolar charge state, the average size of aggregates and the dispersion of particle volume decreased with the increasing of the charge quantities.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.139-146
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• 1991

A generalization of an earlier diffusion model for system subject to continuous wear is presented. It is assumed that the state of the system is modelled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a stationary renewal process and increases the state of the system by a random amount if the state does not exceed a threshold. Various properties of this model are investigated including the distribution of the state of the system at time t, the first passage time to state 0 and the probability that the state of the system exceeds a certain level throughout a specified interval.