• 한국경영과학회지
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• 제6권2호
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• pp.51-55
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• 1981

In both continuous-review and periodic-review non-stationary inventory systems, the non-stationary Poisson demand process and the associated inventory position processes were proved being mutually independent of each other, which lead to the probability distribution of the corresponding net inventory position process in the form of a finite product sum of those two process distributions. It is also discussed how these results can correspond to analytical stochastic inventory cost function formulations in terms of the probability distributions of the processes.

• Journal of the Korean Data and Information Science Society
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• 제8권2호
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• pp.119-125
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• 1997

We handle the stochastic processes of independent and identically distributed random variables. But random variables are usually dependent among themselves in actual life. So in this paper, we find out a new process not satisfying Markov property. We investigate the probability mass functions and study on the probability of the first-passage time. Also we find out the average frequency of continuous successes in from 0 to n time.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 2001년도 추계학술대회 논문집
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• pp.199-202
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• 2001

This article deals with stochastic reliability systems that include a repair facility and unreliable machines: the main facility of working and an auxiliary facility of "super-reserve" machines. The number of super-reserve machines are random number with a arbitrarily distribution and working machines break down exponentially. Defective machines line up for repair, whose durations are arbitrarily distributed. Refurbished machines return to the main facility. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance until all of super-reserve machines are exhausted. Then, the busy period is regenerated. The whole system also falls into the category of closed queues, with more options than those of basic models. The techniques include two-variate Markov and semi-regenerative processes, and a duality principle, to find the probability distribution of the number of intact machines. Explicit formulas obtained demonstrate a relatively effortless use of functionals of the main stochastic characteristics (such as expenses due to repair, maintenance, waiting, and rewards for higher reliability) and optimization of their objective function. Applications include computer networking, human resources, and manufacturing processes.

• 천문학회보
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• 제38권1호
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• pp.45-45
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• 2013

We present a test of the emission statistics of active galactic nuclei (AGN), probing the connection between the red-noise temporal power spectra and multi-modal flux distributions known from observations. We simulate AGN lightcurves under the assumption of uniform stochastic emission processes for different power-law indices of their respective power spectra. For sufficiently shallow slopes (power-law indices beta ${\leq}$ 1.0), the flux distributions (histograms) of the resulting lightcurves are approximately Gaussian. For indices corresponding to steeper slopes (beta ${\geq}$ 1.0), the flux distributions become multi-modal. This finding disagrees systematically with result of recent mm/radio observations. Accordingly, we conclude that the emission from AGN does not necessarily originate from uniform stochastic processes even if their power spectra suggest otherwise. Possible mechanisms include transitions between different activity states and/or the presence of multiple, spatially disconnected, emission regions.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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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.

• 천문학회지
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• 제45권6호
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• pp.147-156
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• 2012

We present a test of the emission statistics of active galactic nuclei (AGN), probing the connection between the red-noise temporal power spectra and multi-modal flux distributions known from observations. We simulate AGN lightcurves under the assumption of uniform stochastic emission processes for different power-law indices of their respective power spectra. For sufficiently shallow slopes (power-law indices (${\beta}{\leq}1$), the flux distributions (histograms) of the resulting lightcurves are approximately Gaussian. For indices corresponding to steeper slopes (${\beta}{\geq}1$), the flux distributions become multi-modal. This finding disagrees systematically with results of recent mm/radio observations. Accordingly, we conclude that the emission from AGN does not necessarily originate from uniform stochastic processes even if their power spectra suggest otherwise. Possible mechanisms include transitions between different activity states and/or the presence of multiple, spatially disconnected, emission regions.

• Communications for Statistical Applications and Methods
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• 제26권1호
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• pp.27-34
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• 2019

We study the effect of detrending on the coherency between two time series processes. Many economic and financial time series variables include nonstationary components; however, we analyze the two most popular cases of stochastic and deterministic trends. We analyze the asymptotic behavior of coherency under incorrect detrending, which includes the cases of first-differencing the deterministic trend process and, conversely, the time trend removal of the unit root process. A simulation study is performed to investigate the finite sample performance of the sample coherency due to incorrect detrending. Our work is expected to draw attention to the possible distortion of coherency when the series are incorrectly detrended. Further, our results can extend to various specification of trends in aggregate time series variables.

• Wind and Structures
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• 제38권1호
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• pp.1-13
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• 2024

In order to effectively simulate nonstationary stochastic turbulent wind fields, four separation hybrid (SEP-H) models are proposed in the present study. Based on the assumption that the lateral turbulence component at one single-point is uncorrelated with the longitudinal and vertical turbulence components, the fluctuating wind is separated into 2nV-1D and nV1D nonstationary stochastic vector processes. The first process can be expressed as double proper orthogonal decomposition (DPOD) or proper orthogonal decomposition and spectral representation method (POD-SRM), and the second process can be expressed as POD or SRM. On this basis, four SEP-H models of nonstationary stochastic turbulent wind fields are developed. In addition, the orthogonal random variables in the SEP-H models are presented as random orthogonal functions of elementary random variables. Meanwhile, the number theoretical method (NTM) is conveniently adopted to select representative points set of the elementary random variables. The POD-FFT (Fast Fourier transform) technique is introduced in frequency to give full play to the computational efficiency of the SEP-H models. Finally, taking a long-span bridge as the engineering background, the SEP-H models are compared with the dimension-reduction DPOD (DR-DPOD) model to verify the effectiveness and superiority of the proposed models.

• 대한수학회지
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• 제19권2호
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• pp.111-116
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• 1983

• 충청수학회지
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• 제8권1호
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• pp.45-53
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• 1995

In this paper, in order to generalize the Theorem[1], it was attempted to generalize the method to prove the Theorem.