• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.865-874
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• 1998

A modulus of continuity on the increments of a two-parameter Gaussian process is obtained via estimating large deviation probability inequalities on the suprema of the Gaussian process.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.379-390
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• 2000

In this paper the limit theorems on lag increments of a Wiener process due to Chen, Kong and Lin [1] are developed to the case of a Gaussian process via estimating upper bounds of large deviation probabilities on suprema of the Gaussian process.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.57-74
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• 1997

Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1215-1230
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• 2005

In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.

• Structural Engineering and Mechanics
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• v.84 no.5
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• pp.651-664
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• 2022

A precise prediction of the ultimate bond strength between rebar and surrounding concrete plays a major role in structural design, as it effects the load-carrying capacity and serviceability of a member significantly. In the present study, Gaussian models are employed for modelling bond strength of ribbed steel bars embedded in concrete. Gaussian models offer a non-parametric method based on Bayesian framework which is powerful, versatile, robust and accurate. Five different Gaussian models are explored in this paper-Gaussian Process (GP), Variational Heteroscedastic Gaussian Process (VHGP), Warped Gaussian Process (WGP), Sparse Spectrum Gaussian Process (SSGP), and Twin Gaussian Process (TGP). The effectiveness of the models is also evaluated in comparison to the numerous design formulae provided by the codes. The predictions from the Gaussian models are found to be closer to the experiments than those predicted using the design equations provided in various codes. The sensitivity of the models to various parameters, input feature space and sampling is also presented. It is found that GP, VHGP and SSGP are effective in prediction of the bond strength. For large data set, GP, VHGP, WGP and TGP can be computationally expensive. In such cases, SSGP can be utilized.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.959-973
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• 2005

In this paper, based on large deviation probabilities on Gaussian random vectors, we obtain Strassen's functional LIL for d-dimensional self-similar Gaussian process in Holder norm via estimating large deviation probabilities for d-dimensional self-similar Gaussian process in Holder norm.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1561-1577
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• 2014

In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in $S_{\alpha}$ [5, 8].

• Journal of the Society of Naval Architects of Korea
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• v.55 no.6
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• pp.466-473
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• 2018

Most frequency domain-based approaches assume that structural response should be a Gaussian random process. But a lot of non-Gaussian processes caused by multi-excitation and non-linearity in structural responses or load itself are observed in many real engineering problems. In this study, the effect of non-Normality on fatigue damages are discussed through case study. The accuracy of four frequency domain methods for non-Gaussian processes are compared in the case study. Power-law and Hermite models which are derived for non-Gaussian narrow-banded process tend to estimate fatigue damages less accurate than time domain results in small kurtosis and in case of large kurtosis they give conservative results. Weibull model seems to give conservative results in all environmental conditions considered. Among the four methods, Benascuitti-Tovo model for non-Gaussian process gives the best results in case study. This study could serve as background material for understanding the effect of non-normality on fatigue damages.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.577-594
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• 2001

In this paper we establish limit theorems on the large and small increments of a two-parameter Gaussian random process on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter Gaussian random process.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.383-391
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• 2006

A characterization of Gaussian process with independent increments in terms of the support of covariance operator is established. We investigate the Girsanov formula for a Gaussian process with independent increments.