• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.297-302
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• 1995

In [1], Cramer introduced the first large deviation theorem at a probability symposium in 1938. Since 1938, there have been many developments in the large deviation theorems.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.381-393
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• 2005

We consider a type of large deviation principle obtained by Freidlin and Wentzell for the solution of Stochastic differential equations in a conuclear space. We are using exponential tail estimates and exit probability of a Ito process. The nuclear structure of the state space is also used.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.244-246
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• 1990

This paper describes the Large Deviation Method for computing the loss-of-load-probability (L.O.L.P.) index for a generating system. Also, we introduce a rule to prevent the initial value from diverging in Newton-Raphson method which we have to use to determine the value of t. By applying the Large Deviation Method to computing the L.O.L.P. index for some representative reliability test systems, it is verified that the Large Deviation Method is generally very accurate and very fast.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.835-845
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• 2017

The $GCF_{\epsilon}$ expansion is a new class of continued fractions induced by the transformation $T_{\epsilon}:(0, 1]{\rightarrow}(0, 1]$: $T_{\epsilon}(x)={\frac{-1+(k+1)x}{1+k-k{\epsilon}x}}$ for $x{\in}(1/(k+1),1/k]$. Under the algorithm $T_{\epsilon}$, every $x{\in}(0,1]$ corresponds to an increasing digits sequences $\{k_n,n{\geq}1\}$. Their basic properties, including the ergodic properties, law of large number and central limit theorem have been discussed in [4], [5] and [7]. In this paper, we study the large deviation for the $GCF_{\epsilon}$ expansion and show that: $\{{\frac{1}{n}}{\log}k_n,n{\geq}1\}$ satisfies the different large deviation principles when the parameter ${\epsilon}$ changes in [-1, 1], which generalizes a result of L. J. Zhu [9] who considered a case when ${\epsilon}(k){\equiv}0$ (i.e., Engel series).

• Journal of the Korean Society for Precision Engineering
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• v.13 no.3
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• pp.49-55
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• 1996

Recently, the necessity for more accurate automatic gauge control has increased of customers' requirement for cold rolled steel sheets with thinner gauge and better gauge quality. Therefore, many cold rolling mills replaced its electric screw down automatic gauge control system with a new hydraulic automatic gauge control system, to ensure closer gauge tolerance. In this paper, The performance of a hydraulic automatic gauge control system for cold rolling has been investigated under industrial conditions. It was investigated that variation of gauge deviation according to the final products thickness, cold rolling speed and pass number, in the actual rolling mill. As a result, it was found that the system enables strip thickness variation to be reduced substantially and caused by poor gauge deviation have been drastically decreased. The test results are as following. The more the exit steel strip thickness is thick, the smaller the aguge deviation rate is large, and the more it is thin, the large the gauge deviation rate is large. Because the gauge deviation is larger at accleration speed and deceleration speed than steady speed, so automatic gauge control system is better to adopt over 50m/min. automatic gauge control system reduces rapidly large thickness deviation.

• Communications of the Korean Mathematical Society
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• v.21 no.3
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• pp.543-558
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• 2006

We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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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.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.155-162
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• 2003

A tandem network in which all nodes have the same load is considered. We derive bounds on the probability that the total population of the tandem network exceeds a large value by using its relation to the stationary distribution. These bounds imply a stronger asymptotic limit than that in the large deviation theory.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.715-723
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• 2003

A tandem network in which all nodes have the same load is considered. We derive bounds on the probability that the total population of the tandem network exceeds a large value by using its relation to the stationary distribution. These bounds imply a stronger asymptotic limit than that in the large deviation theory.