• Honam Mathematical Journal
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• v.15 no.1
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• pp.129-136
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• 1993

In this paper we present of a class infinite M A (moving-average) sequences of multivariate random vectors. We use the theory of positive dependence to show that in a variety of cases the classes of M A sequences are associated. We then apply the association to establish some probability bounds and moment inequalities for multivariate processes.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.133-146
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• 1999

Let {X(t), $t{\geq}0$} be a stochastic integral process represented by stable random measure or multiple Ito-Wiener integrals. Under some conditions, we prove the continuity and self-similarity of these stochastic integral processes. As an application, we get Gaussian chaos which has some shift continuous function.

• The KIPS Transactions:PartC
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• v.12C no.2 s.98
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• pp.281-288
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• 2005

It is generally accepted that self-similar (or fractal) Processes may provide better models for teletraffic in modem computer networks than Poisson processes. f this is not taken into account, it can lead to inaccurate conclusions about performance of computer networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A generator of pseudo-random self similar sequences, based on the SRA (successive random addition) method, is implemented and analysed in this paper. Properties of this generator were experimentally studied in the sense of its statistical accuracy and the time required to produce sequences of a given (long) length. This generator shows acceptable level of accuracy of the output data (in the sense of relative accuracy of the Hurst parameter) and is fast. The theoretical algorithmic complexity is O(n).

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.363-375
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• 2004

In this paper, We show that the bandpass random signals of the form ∑$_{\alpha}$$\alpha$$_{\alpha}$ a Sin(2$\pi$f$_{\alpha}$t + b$_{\alpha}$) where a$_{\alpha}$ being a random number in [0,1], f$_{\alpha}$ a random integer in a given frequency band, and b$_{\alpha}$ a random number in [0, 2$\pi$], generate Gaussian white noise signals and hence they are adequate for simulating Continuous Markov processes. We apply the result to the fluctuation-dissipation formula for the Johnson noise and show that the probability distribution for the long term average of the power of the Johnson noise is a X$^2$ distribution and that the relative error of the long term average is (equation omitted) where N is the number of blocks used in the average.error of the long term average is (equation omitted) where N is the number of blocks used in the average.

• Design & Manufacturing
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• v.14 no.1
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• pp.63-68
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• 2020

Ultra-high brightness and thin displays need to optical micro-patterns which can uniformly diffuse the lights and low loss. The micro random patterns have characteristics to rise the optical efficiency such as light extraction, uniform diffusion. For this reason, various fabrication processes are studied for random patterns. In this study, the micro random patterns were machined by diamond turning which used a controlled cutting tool path with random cutting depth. The machined patterns had random shape and directionality along the circumferential direction. The average width and length of machined random pattern according to rotation radius were 40.13㎛~55.51㎛ and 37.25㎛~59.49㎛, and these results were compared with the designed result. Also, the machining error according to rotation radius in diamond turning using randomly controlled cutting depth was discussed.

• IE interfaces
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• v.11 no.3
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• pp.89-101
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• 1998

The randomness of the input variables in simulation experiments produce output responses which are also realizations of random variables. The random responses make necessary the use of statistical inferences to adequately describe the stochastic nature of the output. The analysis of the simulation output of non-terminating simulations is frequently complicated by the autocorrelation of the output data and the effect of the initial conditions that produces biased estimates. The regenerative method has been developed to deal with some of the problems created by the random nature of the simulation experiments. It provides a simple solution to some tactical problems and can produce valid statistical results. However, not all processes can he modeled using the regenerative method. Other processes modeled as regenerative may not return to a given demarcating state frequently enough to allow for adequate statistical analysis. This paper shows how the state transformation concept was successfully used in a queueing model and a job shop model. Although the first example can be analyzed using the regenerative method. it has the problem of too few recurrences under certain conditions. The second model has the problem of no recurrences. In both cases, the state transformation increase the frequency of the demarcating state. It was shown that time state transformations are regenerative and produce more cycles than the best typical discrete demarcating state in a given run length.

• Journal of The Korean Astronomical Society
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• v.56 no.2
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• pp.287-292
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• 2023

This paper investigates the number of scatterings a photon undergoes in random walks before escaping from a medium. The number of scatterings in random walk processes is commonly approximated as τ + τ² in the literature, where τ is the optical thickness measured from the center of the medium. However, it is found that this formula is not accurate. In this study, analytical solutions in sphere and slab geometries are derived for both optically thin and optically thick limits, assuming isotropic scattering. These solutions are verified using Monte Carlo simulations. In the optically thick limit, the number of scatterings is found to be 0.5 τ² and 1.5 τ² in a sphere and slab, respectively. In the optically thin limit, the number of scatterings is ≈ τ in a sphere and ≈ τ (1 - γ - ln τ + τ) in a slab, where γ ≃ 0.57722 is the Euler-Mascheroni constant. Additionally, we present approximate formulas that reasonably reproduce the simulation results well in intermediate optical depths. These results are applicable to scattering processes that exhibit forward and backward symmetry, including both isotropic and Thomson scattering.

• Journal of Korea Water Resources Association
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• v.32 no.1
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• pp.61-70
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• 1999

The two-dimensional Random-Walk model in which fluid and pollutant particles are tracked using statistical concept was developed to simulate dispersion processes in natural streams. The calibration of the model shows that the error decreases as the number of grid increases, and/or the number of particles in each grid increases. The proposed model is tested against the dispersion data collected in the Grand River, Canada. The simulation results show that the 2-D Random-Walk model describes two-dimensional mixing phenomena occurred in the irregular meandering stream very accurately.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.22 no.1E
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• pp.26-32
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• 2003

We propose new time-frequency (TF) tools for analyzing linear time-varying (LTV) systems and nonstationary random processes showing hyperbolic TF structure. Obtained through hyperbolic warping the narrowband Weyl symbol (WS) and spreading function (SF) in frequency, the new TF tools are useful for analyzing LTV systems and random processes characterized by hyperbolic time shifts. This new TF symbol, called the hyperbolic WS, satisfies the hyperbolic time-shift covariance and scale covariance properties, and is useful in wideband signal analysis. Using the new, hyperbolic time-shift covariant WS and 2-D TF kernels, we provide a formulation for the hyperbolic time-shift covariant TF symbols, which are 2-D smoothed versions of the hyperbolic WS. We also propose a new interpretation of linear signal transformations as weighted superposition of hyperbolic time shifted and scale changed versions of the signal. Application examples in signal analysis and detection demonstrate the advantages of our new results.