• 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 Korea Institute of Information and Communication Engineering
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• v.14 no.6
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• pp.1469-1475
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• 2010

This paper presents a problem of existing encryption methods using pseudo-random numbers based on MLCA or complemented MLCA and proposes a method to resolve this problem. The existing encryption methods have a problem which the edge of original image appear on encrypted image because the image have color similarity of adjacent pixels. In this proposed method, we transform the value and spatial coordinates of all pixels by using pseudo-random numbers based on MLCA. This method can resolve the problem of existing methods and improve the level of encryption by encrypting pixel coordinates and pixel values of original image. The effectiveness of the proposed method is proved by conducting histogram and key space analysis.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.235-249
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• 2012

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.419-427
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• 2004

In this paper we establish the Hajeck-Renyi type inequality and derive the strong law of large numbers for asymptotically quadrant sub-independent random variables.

• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.291-296
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• 2001

For randomly indexed sums of the form (Equation. See Full-text), where {X(sub)ni, i$\geq$1, n$\geq$1} are random variables, {N(sub)n, n$\geq$1} are suitable conditional expectations and {b(sub)n, n$\geq$1} are positive constants, we establish a general weak law of large numbers. Our result improves that of Hong [3].

• East Asian mathematical journal
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• v.36 no.1
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• pp.25-34
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• 2020

The classical limit theorems like strong law of large numbers, central limit theorems and law of iterated logarithms are fundamental theories in probability and statistics. These limit theorems are proved under additivity of probabilities and expectations. In this paper, we investigate strong law of large numbers under sub-linear expectation which generalize the classical ones. We give strong law of large numbers under sub-linear expectation with respect to the partial sums and some conditions similar to Petrov's. It is an extension of the classical Chung type strong law of large numbers of Jardas et al.'s result. As an application, we obtain Chung's strong law of large number and Marcinkiewicz's strong law of large number for independent and identically distributed random variables under the sub-linear expectation. Here the sub-linear expectation and its related capacity are not additive.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.123-131
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• 2000

This paper concerns with the consistent estimator for the fuzzy expectation of a random variable taking values in the space F($R^p$) of upper semicontinuous convex fuzzy subsets of $R^p$ with compact support. We introduce the concept of a fuzzy sample mean and show that the fuzzy sample mean is a strong consistent estimator for the fuzzy expectation. Some examples are given to illustrate the main result.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.205-219
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• 2002

We deride formulas for the expected values $\mu$(n) of the independent domination numbers of a random planted plane tree and a random trivalent tree with n vertices, respectively, and we determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.53-63
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• 1993

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.