• Journal of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.225-239
• /
• 2006

In [5], Csorgo and Zitikis exposed the strong $uniform-over-[0,\;{\infty}]$ consistency, and weak $uniform-over-[0,\;{\infty}]$ approximation of the empirical mean residual life process by employing weight functions. We carry on the uniform asymptotic behaviors of the empirical mean residual life process over the whole positive half line by representing the process as an integral form. We compare our results with those of Yang [15], Hall and Wellner [8], and Csorgo and Zitikis [5].

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.403-412
• /
• 2004

We obtain a kernel quantile process based on the kernel quantile estimator and prove the uniform consistency of the kernel quantile process by developing that of the usual sample quantile process. We apply our result to the classical kernel type processes.

• Communications for Statistical Applications and Methods
• /
• v.18 no.2
• /
• pp.229-236
• /
• 2011

A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general L$\'{e}$vy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential ${\alpha}$-mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.

• Journal of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.935-946
• /
• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• Communications for Statistical Applications and Methods
• /
• v.19 no.5
• /
• pp.639-646
• /
• 2012

The exponential continuous time GARCH(p,q) model for financial assets suggested by Haug and Czado (2007) is considered, where the log volatility process is driven by a general L$\acute{e}$vy process and the price process is then obtained by using the same L$\acute{e}$vy process as driving noise. Uniform ergodicity and ${\beta}$-mixing property of the log volatility process is obtained by adopting an extended generator and drift condition.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
• /
• v.26 no.11
• /
• pp.97-103
• /
• 2012

The basic processing unit for instant ramen noodles includes mixing, rolling, boiling, frying, cooling, and packing processes. For uniform thickness of dough sheets in rolling process, the roll-gap in rolling process needs to keep uniform thickness of flour sheets in spite of different kinds of raw materials. In this paper, we have developed a roll gap adjustment system using a PLC (Programmable Logic Controller) with a touch panel and an AC servo-mechanism to make dough sheets with a good gluten starch-network structure and uniform thickness and to contribute to process standardization by transferring from tacit knowledge of skilled workers to explicit knowledge. The developed system can adjust the roll gap in units of 0.01mm and correspond to various product items which have different thickness specification by recalling the presetting values of the desired thickness from database.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.373-383
• /
• 2003

We investigate a uniform local asymptotic normality for likelihood ratio processes based on an independent and identically distributed local asymptotic problem. Our tool is an empirical process theory.

• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.581-595
• /
• 1999

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.24 no.7
• /
• pp.553-559
• /
• 2012

A plate-fin heat exchanger is a type of heat exchanger widely used in air conditioners, and tubes and fins are tightly assembled by the mechanical expansion process of tubes. The tube expansion process deforms the grooves inside the tube, and the groove shapes also affect the adhesion between tubes and fins. In this study, the adhesion and heat transfer performance affected by the tube expansion of the non-uniform groove shape tube with different heights are investigated by both analysis and experiments. From the analysis method, it was shown that the contact pressure of non-uniform groove tube is higher than that of the uniform groove tube, and the most appropriate high groove number of the non-uniform groove tube is designed for the maximum contact pressure. From the experimental results, the decreasing rate of the condensation heat transfer coefficient is smaller in the non-uniform groove tube with different heights, compared to the conventional uniform groove tube. Also, the air-side heat transfer coefficient of the non-uniform groove tube with different heights is higher than that of the uniform groove tubes.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.6
• /
• pp.1565-1571
• /
• 2017

The standard logistic map is an iterative function, which forms a discrete-time dynamic system. The chaotic logistic map is a kind of ergodic map defined over the unit interval. In this paper we study the limiting behaviors on the several processes induced by the chaotic logistic map. We derive the law of large numbers for the process induced by the chaotic logistic map. We also derive the uniform law of large numbers for this process. When deriving the uniform law of large numbers, we study the role of bracketing of the indexed class of functions associated with the process. Then we apply the idea of DeHardt (1971) associated with the bracketing method to the process induced by the logistic map. We finally illustrate an application to Monte Carlo integration.