• 대한수학회보
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• 제47권6호
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• pp.1139-1153
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• 2010

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

• 대한수학회지
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• 제55권3호
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• pp.575-591
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• 2018

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

• 대한수학회논문집
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• 제23권1호
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• pp.133-140
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• 2008

Let {${\xi}_k,\;k\;{\in}\;{\mathbb{Z}}$} be a strictly stationary associated sequence of H-valued random variables with $E{\xi}_k\;=\;0$ and $E{\parallel}{\xi}_k{\parallel}^2\;<\;{\infty}$ and {$a_k,\;k\;{\in}\;{\mathbb{Z}}$} a sequence of linear operators such that ${\sum}_{j=-{\infty}}^{\infty}\;{\parallel}a_j{\parallel}_{L(H)}\;<\;{\infty}$. For a linear process $X_k\;=\;{\sum}_{j=-{\infty}}^{\infty}\;a_j{\xi}_{k-j}$ we derive that {$X_k} fulfills the functional central limit theorem.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권2호
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• pp.139-147
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• 2004

Let {<$\mathds{X}_t$} be an m-dimensional linear process of the form $\mathbb{X}_t\;=\sumA,\mathbb{Z}_{t-j}$ where {$\mathbb{Z}_t$} is a sequence of stationary m-dimensional negatively associated random vectors with $\mathbb{EZ}_t$ = $\mathbb{O}$ and $\mathbb{E}\parallel\mathbb{Z}_t\parallel^2$ < $\infty$. In this paper we prove the central limit theorems for multivariate linear processes generated by negatively associated random vectors.

• 호남수학학술지
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• 제30권1호
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• pp.9-20
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• 2008

Let ${X_i{\mid}i{\geq}1}$ be a strictly stationary sequence of associated random variables with mean zero and let ${\sigma}^2=EX_1^2+2\sum\limits_{j=2}^\infty{EX_1}{X_j}$ with 0 < ${\sigma}^2$ < ${\infty}$. Set $S_n={\sum\limits^n_{i=1}^\{X_i}$, the precise asymptotics for ${\varepsilon}^{{\frac{2(r-p)}{2-p}}-1}\sum\limits_{n{\geq}1}n^{{\frac{r}{p}}-{\frac{1}{p}}+{\frac{1}{2}}}P({\mid}S_n{\mid}{\geq}{\varepsilon}n^{{\frac{1}{p}}})$,${\varepsilon}^2\sum\limits_{n{\geq}3}{\frac{1}{nlogn}}p({\mid}Sn{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ and ${\varepsilon}^{2{\delta}+2}\sum\limits_{n{\geq}1}{\frac{(loglogn)^{\delta}}{nlogn}}p({\mid}S_n{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ as ${\varepsilon}{\searrow}0$ are established under the suitable conditions.

• 대한수학회지
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• 제35권3호
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• pp.741-753
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• 1998

Let G(*) be a Borel function applied to a stationary long memory sequence {X$_{i}$} of standard Gaussian random variables. Focusing on the process {G(X$_{i}$)}, the present paper establishes the almost sure representation for the empirical quantile process, that is, Bahadur's representation, and for the empirical process with respect to sample mean. Statistical applications of the representations are also addressed.sed.

• 대한수학회논문집
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• 제22권2호
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• pp.315-321
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• 2007

We show an exponential inequality for negatively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. To obtain this result we use a truncation technique together with a block decomposition of the sums. We also identify a convergence rate for the strong law of large number.

• Journal of Communications and Networks
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• 제17권1호
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• pp.1-11
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• 2015

In this paper, the transmission of an improper-complex second-order stationary data sequence is considered over a strictly band-limited frequency-selective channel. It is assumed that the transmitter employs linear modulation and that the channel output is corrupted by additive proper-complex cyclostationary noise. Under the average transmit power constraint, the problem of minimizing the mean-squared error at the output of a widely linear receiver is formulated in the time domain to find the optimal transmit and receive waveforms. The optimization problem is converted into a frequency-domain problem by using the vectorized Fourier transform technique and put into the form of a double minimization. First, the widely linear receiver is optimized that requires, unlike the linear receiver design with only one waveform, the design of two receive waveforms. Then, the optimal transmit waveform for the linear modulator is derived by introducing the notion of the impropriety frequency function of a discrete-time random process and by performing a line search combined with an iterative algorithm. The optimal solution shows that both the periodic spectral correlation due to the cyclostationarity and the symmetric spectral correlation about the origin due to the impropriety are well exploited.

• 한국음향학회지
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• 제9권2호
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• pp.42-52
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• 1990

음향전파 측정에 상호상관법(직접법과 M계열 변조상관법)을 이용하므로서 임펄스 입력에 의한 경우와 같은 결과를 얻을 수 있다는 것과, 또 상호상관법의 특징인 외란노이즈의 영향을 줄일 수 있었던 것 등을 건축음향분야에서 측정계를 대상으로 하여 이론적으로 정리하였다. 또 이들 계측법을 응용하여 흡음재료의 사입사 흡음특성의 측정, 실의 단독 단음응답 및 잔향감쇄 과정의 측정, 음압레벨 분포, 차음성능 등을 측정하고 여러 건축음향측정에서 이들 방법이 유효하다는 것을 실험적으로 확인하였다.

• Journal of the Korean Data and Information Science Society
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• 제22권4호
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• pp.631-641
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• 2011

과거 시행의 승패 결과에 의해 현재 시행의 승패 확률이 결정되는 과거 의존 파론도 게임을 고려한다. 여러 명의 게임자들이 과거 의존 파론도 게임을 구성하는 공정한 두 게임 중에서 한 게임을 임의로 선택하는 전략과 매 시행 때마다 현재의 상태를 이용하여 그 기대상금이 최대인 게임을 선택하는 전략을 비교한다. 현재의 상태를 고려하지 않고 임의적으로 게임을 선택하는 전략은 점차 기대상금이 양수가 되어 결국 이기는 게임이 되는 반면에 현재의 상태를 이용하여 최적의 게임을 선택하는 전략은 게임이 진행될수록 오히려 기대상금이 0으로 일정하게 되는 역설적인 현상이 나타남을 확인하고, 이러한 역설적인 현상이 발생하는 확률 모수의 범위를 찾는다.