• 대한수학회지
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• 제36권3호
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• pp.509-525
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• 1999

In this paper we obtain sharp upper and lower bounds of samll ball and large deviation probabilities for the increments of Gaussian processes with stationary increments, whose results are essential to establish Chung type laws of iteratted logarithm.

• 대한수학회보
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• 제35권2호
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• pp.209-225
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• 1998

In this paper we obtain sharp upper and lower bounds of small ball oprobabilities for Gaussian processes with stationary increments, whose results are essential to estabilish Chung type laws of iterated logarithm.

• 대한수학회지
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• 제46권2호
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• pp.347-361
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• 2009

In this paper, by estimating small ball probabilities of $l^{\infty}$-valued Gaussian processes, we investigate Chung-type law of the iterated logarithm of $l^{\infty}$-valued Gaussian processes. As an application, the Chung-type law of the iterated logarithm of $l^{\infty}$-valued fractional Brownian motion is established.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.193-211
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• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

• Tribology and Lubricants
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• 제30권4호
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• pp.199-204
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• 2014

Various heat-treated and surface coating methods are used to mitigate abrasion in sliding machine parts. The most cost effective of these methods involves hard coatings such as diamond-like carbon (DLC). DLC has various advantages, including a high level of hardness, low coefficient of friction, and low wear rate. In practice, a supporting layer is generally inserted between the DLC layer and the steel substrate to improve the load carrying capacity. In this study, an indentation and sliding contact problem involving a small, hard, spherical particle and a DLC-coated steel surface is modeled and analyzed using a nonlinear finite element code, MARC, to investigate the influence of the supporting layer thickness on the coating characteristics and the related coating failure mechanisms. The results show that the amount of plastic deformation and the maximum principal stress decrease with an increase in the supporting layer thickness. However, the probability of the high tensile stress within the coating layer causing a crack is greatly increased. Therefore, in the case of DLC coating with a supporting layer, fatigue wear can be another important cause of coating layer failure, together with the generally well-known abrasive wear.