• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.443-455
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• 2017

In this paper, we study ARCH(${\infty}$) models with either geometrically decaying coefficients or hyperbolically decaying coefficients. Most popular autoregressive conditional heteroscedasticity (ARCH)-type models such as various modified generalized ARCH (GARCH) (p, q), fractionally integrated GARCH (FIGARCH), and hyperbolic GARCH (HYGARCH). can be expressed as one of these cases. Sufficient conditions for $L_2$-near-epoch dependent (NED) property to hold are established and the functional central limit theorems for ARCH(${\infty}$) models are proved.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.299-305
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• 2003

The central limit theorems are obtained for stationary linear processes of the form Xt = (equation omitted), where {$\varepsilon$t} is a strictly stationary sequence of random variables which are either linearly positive quad-rant dependent or associated and {aj} is a sequence of .eat numbers with (equation omitted).

• 대한수학회논문집
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• 제14권3호
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• pp.629-629
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• 1999

• 한국지능시스템학회논문지
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• 제15권3호
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• pp.337-342
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• 2005

이 논문에서는 서로 독립이고 동일한 분포를 갖는 집합치 랜덤 변수의 합에 대한 중심극한정리의 일반화로서, 수준연속인 퍼지 집합치 랜덤 변수의 합에 대한 중심극한정리를 연구하였다.

• 대한수학회지
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• 제58권4호
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• pp.819-833
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• 2021

Hawkes process is a self-exciting simple point process with clustering effect whose jump rate depends on its entire past history and has been widely applied in insurance, finance, queueing theory, statistics, and many other fields. Seol [27] proposed the inverse Markovian Hawkes processes and studied some asymptotic behaviors. In this paper, we consider an extended inverse Markovian Hawkes process which combines a Markovian Hawkes process and inverse Markovian Hawkes process with features of several existing models of self-exciting processes. We study the limit theorems for an extended inverse Markovian Hawkes process. In particular, we obtain a law of large number and central limit theorems.

• 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.

• 대한수학회지
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• 제61권4호
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• pp.713-742
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• 2024

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a σ-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.

• 대한수학회논문집
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• 제14권3호
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• 대한수학회논문집
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• 제33권2호
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• pp.605-618
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• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• 대한수학회지
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• 제36권5호
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• pp.923-943
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• 1999

In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let f : R+ longrightarrow R be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.