• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.504-512
• /
• 1994

A simple proof for the random central limit theorem is given for a family of stationary linear lattice processes, which belogn to a class of 2 dimensional random fields, applying the Beveridge and Nelson decomposition in time series context. The result is an extension of Fakhre-Zakeri and Fershidi (1993) dealing with the linear process in time series to the case of the linear lattice process with 2 dimensional indices.

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

• Honam Mathematical Journal
• /
• v.32 no.1
• /
• pp.91-99
• /
• 2010

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.171-189
• /
• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• Journal of the Korean Statistical Society
• /
• v.23 no.1
• /
• pp.39-51
• /
• 1994

Some exponential moment inequalities for sub-gaussian random variables are studied in this paper. These inequalities are used to obtain laws of large numbers for random variable and random elements in $L^1(R)$.

• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.527-543
• /
• 2014

The theory of random variable structures was first studied by Ben Yaacov in [2]. Ben Yaacov's axiomatization of the theory of random variable structures used an early result on the completeness theorem for Lukasiewicz's [0, 1]-valued propositional logic. In this paper, we give an elementary approach to axiomatizing the theory of random variable structures. Only well-known results from probability theory are required here.

• Journal of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1075-1088
• /
• 2014

We consider random fractal sets with random recursive constructions in which the contracting vectors have different distributions at different stages. We prove that the random fractal associated with such construction has a constant packing dimension almost surely and give an explicit formula to determine it.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1539-1554
• /
• 2013

In this paper, we extend Donsker's invariance principle to the case of random partial sums processes based on a double sequence of row-wise i.i.d. random variables.

• Korean Journal of Mathematics
• /
• v.26 no.1
• /
• pp.129-141
• /
• 2018

In this slush pile, we introduce a new kind of variational inclusions problem stated as random extended generalized nonlinear variational inclusions for random fuzzy mappings. We construct an iterative scheme for the this variational inclusion problem and also discuss the existence of random solutions for the problem. Further, we show that the approximate solutions achieved by the generated scheme converge to the required solution of the problem.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10a
• /
• pp.832-835
• /
• 1987

This paper proposes a new method of generating binary random sequences using a randomly sampled M-sequence. In this paper two methods of sampling are proposed. Expected values of the autocorrelation function of the sequence generated by these methods are calculated theoretically. From the results of computer simulation, it is shown that using these methods, we can get binary random sequences which have good random properties.