• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.573-583
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• 2001

A condition in which the covariances of Matheron's variogram estimators are expressed in a simple form is reviewed. An asymptotic property of the covariances of the variogram estimators is examined, and a sufficient condition that guaranties the finiteness of the asymptotic variance of the normalized variogram estimators is provided.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.2
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• pp.165-170
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• 2019

$C^1$ generically, if a diffeomorphism $f:M{\rightarrow}M$ of a closed smooth Riemannian manifold M has the asymptotic average shadowing property or the average shadowing property then f has a decomposition property.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.617-623
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• 2010

Let p be a hyperbolic periodic point of f, and let ${\Lambda}(p)$ be a closed set which containing p. In this paper, we show that $C^1$-generically, if $f{\mid}_{{\Lambda}(p)}$ has the $C^1$-stably asymptotic average shadowing property, then it admits a dominated splitting.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.27-33
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• 2012

Let $f$ be a difeomorphism of a closed $n$ -dimensional smooth manifold M, and $p$ be a hyperbolic periodic point of $f$. Let ${\Lambda}(p)$ be a closed set which containing $p$. In this paper, we show that (i) if $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$, then ${\Lambda}(p)$ is the chain component which contains $p$. (ii) suppose $f$ has the asymptotic average shadowing property on ${\Lambda}(p)$. Then if $f|_{\Lambda(p)}$ has the $C^{1}$-stably shadowing property then it is hyperbolic.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2016

This paper shows that the solutions to the perturbed functional dierential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic property. To sRhow these properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y^{\prime}=f(t,y)$.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.1-11
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• 2016

This paper shows that the solutions to nonlinear perturbed functional differential system $$y^{\prime}=f(t,y)+{\int}^t_{t_0}g(s,y(s),Ty(s))ds+h(t,y(t))$$ have the asymptotic property by imposing conditions on the perturbed part ${\int}^t_{t_0}g(s,y(s),Ty(s))ds,h(t,y(t))$ and on the fundamental matrix of the unperturbed system y' = f(t, y).

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.545-556
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• 2009

We show that two notions of asymptotic equilibrium and asymptotic equilibrium in variation for nonlinear differential systems are equivalent via $t_{\infty}$-similarity of associated variational systems. Moreover, we study the asymptotic equivalence between nonlinear system and its variational system.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.461-466
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• 2018

$Let\;f:X{\rightarrow}X$ be a continuous surjection of a compact metric space X and let ${\sigma}_f:X_f{\rightarrow}X_f$ be the shift map on the inverse limit space $X_f$ constructed by f. We show that if a continuous surjective map f has some shadowing properties: the asymptotic average shadowing property, the average shadowing property, the two side limit shadowing property, then ${\sigma}_f$ also has the same properties.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).