• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.17-25
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• 2006

We generalize the results about eigenvalues of random walks on central hyperplane arrangements computed by Bidigare, Hanlon and Rockmore to the cases of random walks on oriented matroids.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.25-33
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• 2001

Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.153-159
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• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1241-1251
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• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.279-287
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• 1995

Let $F$ be a set of distributions on R with the topology of weak convergence, and let $A$ be the $\sigma$-field generated by the open sets. We denote by $F_1^\infty$ the space consisting of all infinite sequence $(F_1, F_2, \cdots), F_n \in F and R_1^\infty$ the space consisting of all infinite sequences $(x_1, x_2, \cdots)$ of real numbers. Take the $\sigma$-field $F_1^\infty$ to be the smallest $\sigma$-field of subsets of $F_1^\infty$ containing all finite-dimensional rectangles and take $B_1^\infty$ to be the Borel $\sigma$-field $R_1^\infty$.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.118-130
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• 1982

Random walks as specia Markov stochastic processes have received particular attention in recent years. Not only the applicability of the theory already developed but also its extension within the frame work of probability measures on algebraic-topological structures such as semigroups, groups and linear spaces became a new challenge for research work in the field. At the same time new insights into classical problems were obtained which in various cases lead to a more efficient presentation of the subject. Consequently the teaching of random walks at all levels should profit from the recent development.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2017.11a
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• pp.133-135
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• 2017

본 논문에서는 스테레오 영상을 이용하여 외삽 시점 영상 생성 시 발생하는 홀을 채우는 방법을 제안한다. 스테레오 영상에 3D 워핑을 이용하여 다수의 시점을 생성할 수 있다. 하지만 이 방법은 보이지 않는 시점에서의 영역을 완벽히 복원할 수 없기 때문에 필연적으로 홀이 발생한다. 홀을 채우기 위해 먼저 홀 영역의 경계를 Random Walks 알고리즘을 이용하여 전경과 배경으로 구분한다. 그리고 홀을 배경 성분에 해당하는 영역만을 이용하여 채우게 된다. 홀 채움 과정에서는 패치 내의 홀의 비율과 컬러와 깊이 영상의 텍스처에 대한 복잡도를 정의하고 패치 별로 우선순위를 계산하여 높은 순위의 패치로 홀을 채우게 된다. 실험 결과 제안하는 기법이 홀을 효과적으로 채우는 것을 확인하였다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.63-66
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• 2009

Automatic segmentation of foreground from background in video sequences has attracted lots of attention in computer vision. This paper proposes a novel framework for the background subtraction that the foreground is segmented from the background by directly subtracting a background image from each frame. Most previous works focus on the extraction of more reliable seeds with threshold, because the errors are occurred by noise, weak color difference and so on. Our method has good segmentations from the approximate seeds by using the Random Walks with Restart (RWR). Experimental results with live videos demonstrate the relevance and accuracy of our algorithm.

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.233-239
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• 1994

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.293-301
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• 1995

Sums of independent random variables $S_n = X_1 + \cdots + X_n$ are considered, where the $X_n$ are chosen according to a stationary process of distributions. For $c > 0$, let $t_c$ be the smallest positive integer n such that $$\mid$S_n$\mid$ > cn^{\frac{1}{2}}$. In this set up we are concerned with finiteness of expectation of $t_c$ and we have some results of sign-invariant process as applications.