• 대한수학회지
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• 제35권3호
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• 대한수학회논문집
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• 제10권4호
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• pp.963-974
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• 1995

We formulate central limit theorems for non-linear functionals of stationary Gaussian vector processes with long-range dependence.

• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.11-20
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• 2003

Let｛Ｘt｝be an m-dimensional linear process of the form (equation omitted), where｛Zt｝is a sequence of stationary m-dimensional weakly associated random vectors with EZt = O and E∥Zt∥$^2$＜$\infty$. We Prove central limit theorems for multivariate linear processes generated by weakly associated random vectors. Our results also imply a functional central limit theorem.

• Journal of the Korean Data and Information Science Society
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• 제16권2호
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• pp.359-369
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• 2005

Central limit theorem is known as one of the most important limit theorem in statistics and probability. This paper provides a dynamic MS Excel program that demonstrates computer simulation of various types of central limit theorems. Our result will be of great use for better understanding of central limit theorems.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.

• Communications for Statistical Applications and Methods
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• 제20권3호
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• pp.193-197
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• 2013

Almost sure central limit theorems are established for a stationary bootstrap sample mean of strong mixing processes. Both weak and strong consistencies are obtained.

• 대한수학회지
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• 제56권4호
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• pp.935-946
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• 2019

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history. We consider Hawkes processes with uniform immigrants which is a special case of the Hawkes processes with renewal immigrants. We study the limit theorems for Hawkes processes with uniform immigrants. In particular, we obtain a law of large number, a central limit theorem, and a large deviation principle.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• 대한수학회논문집
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• 제29권2호
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• pp.351-358
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• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• 대한수학회보
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• 제54권3호
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• pp.839-874
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• 2017

Our goal is to establish and prove the almost sure central limit theorems for some order statistics $\{M_n^{(k)}\}$, $k=1,2,{\ldots}$, formed by stochastic processes ($X_1,X_2,{\ldots},X_n$), $n{\in}N$, the distributions of which are defined by certain Archimedean copulas. Some properties of generators of such the copulas are intensively used in our proofs. The first class of theorems stated and proved in the paper concerns sequences of ordinary maxima $\{M_n\}$, the second class of the presented results and proofs applies for sequences of the second largest maxima $\{M_n^{(2)}\}$ and the third (and the last) part of our investigations is devoted to the proofs of the almost sure central limit theorems for the k-th largest maxima $\{M_n^{(k)}\}$ in general. The assumptions imposed in the first two of the mentioned groups of claims significantly differ from the conditions used in the last - the most general - case.