• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.237-264
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• 2021

In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

• Journal of the Korean Operations Research and Management Science Society
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• v.42 no.1
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• pp.19-28
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• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.463-471
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• 2000

A central limit theorem is obtained for stationary linear process Xt = aj$\varepsilon$t-j, where {$\varepsilon$t} a strictly stationary associated sequence with Et < and {aj} is a sequence of real numbers with <. A functional central limit theorem is also derived.

• Structural Engineering and Mechanics
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• v.82 no.3
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• pp.325-341
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• 2022

Previous major earthquakes indicated that the earthquake induced ground motions are typical non-stationary processes, which are non-stationary in both amplification and frequency. For the convenience of aseismic design and analysis, it usually assumes that the ground motions at structural supports are stationary processes. The development of time-frequency analysis technique makes it possible to evaluate the non-stationary responses of engineering structures subjected to non-stationary inputs, which is more general and realistic than the analysis method commonly used in engineering. In this paper, the wavelet-based stochastic vibration analysis methodology is adopted to calculate the non-stationary responses of multi-support structures. For comparison, the stationary response based on the standard random vibration method is also investigated. A frame structure and a two-span bridge are analyzed. The effects of non-stationary spatial ground motion and local site conditions are considered, and the influence of structural property on the structural responses are also considered. The analytical results demonstrate that the non-stationary spatial ground motions have significant influence on the response of multi-support structures.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.04a
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• pp.61-68
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• 1999

In the nonlinear dynamic structural analysis the given ground excitation as an input should be well defined. Because of the lack of recorded accelerograms in Korea it is required to generate an artificial earthquake by a stochastic model of ground excitation with various dynamic properties rather than recorded accelerograms. It is well known that earthquake motions are generally non-stationary with time-varying intensity and frequency content. Many researchers have proposed non-stationary random process models. Yeh and Wen (1990) proposed a non-stationary modulation function and a power spectral density function to describe such non-stationary characteristics. Satio and Wen(1994) proposed a non-stationary stochastic process model to generate earthquake ground motions which are compatible with design reponse spectrum at sites in Japan. this paper shows the process to modify power spectrum compatible with target design response spectrum for generating of nonstationary artificial earthquake ground motions. Target reponse spectrum is chosen by ATC14 to calibrate the response spectrum according to a give recurrence period.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.153-158
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• 2001

A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.715-722
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• 2003

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}=\;{\Sigma_{j=0}}^{\infty}a_{j}{\epsilon}_{t-j}, where {${\in}_{t}$｝is a strictly stationary associated sequence of random variables with $E_{{\in}_t}{\;}={\;}0.{\;}E({\in}_t^2){\;}<{\;}{\infty}{\;}and{\;}{a_j}$ is a sequence of real numbers with (equation omitted). A central limit theorem for a stationary linear process generated by stationary associated processes is also discussed.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.504-512
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• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.2
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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 Mathematical Society
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• v.39 no.1
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• pp.119-126
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• 2002

For a stationary multivariate linear process of the form X$_{t}$ = (equation omitted), where {Z$_{t}$ : t = 0$\pm$1$\pm$2ㆍㆍㆍ} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Z$_{t}$) = O and E∥Z$_{t}$∥ $^2$< $\infty$, we prove a central limit theorem.theorem.