• Journal of Institute of Control, Robotics and Systems
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• v.11 no.6
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• pp.492-495
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• 2005

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded control. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We show that our estimate is always better than the estimate of [3].

• East Asian mathematical journal
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• v.34 no.1
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• pp.1-16
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• 2018

We study an optimization problem for hyperbolic absolute risk aversion (HARA) utility function under two-factor Heston's stochastic volatility model. It is not possible to obtain an explicit solution because our financial market model is complicated. However, by using asymptotic analysis technique, we find the explicit forms of the approximations of the optimal value function and the optimal strategy for HARA utility function.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.449-463
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• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.153-165
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• 2003

This paper considers the likelihood ratio test statistic based on nonlinear regression quantiles estimators in order to test of hypothesis about the regression parameter $\theta_o$ and derives asymptotic distribution of proposed test statistic under the null hypothesis and a sequence of local alternative hypothesis. The paper also investigates asymptotic relative efficiency of the proposed test to the test based on the least squares estimators or the least absolute deviation estimators and gives some examples to illustrate the application of the main result.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.138-143
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• 1993

A well-defined relative degree, which is one of the basic assumptions in adaptive control or nonlinear synthesis problems, is addressed. It is shown that this is essentially a necessary condition for asymptotic tracking in discrete-time nonlinear systems. To show this, tracking problems are defined, and a local linear input-output behavior of a discrete-time system is introduced in relation to a well-defined relative degree. It is then shown that if a plant is invertible and accessible from the origin and a compensator solves the local asymptotic tracking problem, then the plant necessarily has a well-defined relative degree at the origin.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.15-22
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• 2004

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.173-177
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• 1998

This paper presents the asymptotic relative efficiency of the nonparametric estimator relative to the parametric maximum likelihood estimator of the reliability function under the proportional hazards model of random censorship. Also we examine the efficiency loss due to censoring proportions and misson times.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.12.1-12
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• 2003

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation On the modulus of continuity This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.47-56
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• 1997

The asymptotic distribution of the extended Yule-Walker estimates of a mixed ARMA process is derived. Also, a recursive algorithm is derived to calculate the extended Yule-Walker estimates recursively, which is a generalization of the Levinson-Durbin algorithm.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.13-15
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• 2000

In this paper, we deal with the asymptotic properties of the regression quantile estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears fer a time series analysis, we study the strong consistency and asymptotic normality of regression quantile ostinators.