• Honam Mathematical Journal
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• v.16 no.1
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• pp.111-117
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• 1994

In this note we prove a functional central. limit theorem for LPQD sequences, statisfying some moment conditions. No stationarity is required. Our results imply an extension of Birkel's functional central limit theorem for associated processt'S to an LPQD sequence and an improvement of Birkel's functional central limit theorem for LPQD sequences.

• Journal of the Korean Statistical Society
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• v.32 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1033-1038
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• 1997

A functional central limit theorem for a class of nonlinear stationary Markov processes which are geometrically Harris ergodic is derived.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.707-714
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• 1995

In this note, we extend the concepts of linearly positive quadrant dependence to the random vectors and prove a functional central limit theorem for positively quadrant dependent sequence of $R^d$-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition. This result is an extension of a functional central limit theorem for weakly associated random vectors of Burton et al. to positive quadrant dependence case.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1117-1122
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• 1996

A class of nonlinear Markov processes on the real line is considered, and a functional central limit theorem is proved for the functions of bounded variation on the real line by identifying a broad subset of the range of the generator.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.411-418
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• 1997

In this note we prove a functional central limit theorem for nonstationary linearly positive quadrant dependent random fields. We extend it to the case of random measures.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.45-53
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• 2000

Existence of a unique invariant probability is considered for a class of Markov processes which may not be irreducible and a functional central limit theorem for a class of nonlinear irreducible uniformly ergodic processes is derived as well.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.339-345
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• 2013

In this paper, we give a tractable sufficient condition for functional central limit theorem to hold in Markov switching ARMA (p, q) model.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.495-504
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• 2001

In this paper we consider the (generalized) autoregressive model with conditional heteroscedasticity (ARCH/GARCH models). We willing give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.715-722
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• 2003

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}=\;{\Sigma_{j=0}}^{\infty}a_{j}{\epsilon}_{t-j}, where {${\in}_{t}$｝is a strictly stationary associated sequence of random variables with $E_{{\in}_t}{\;}={\;}0.{\;}E({\in}_t^2){\;}<{\;}{\infty}{\;}and{\;}{a_j}$ is a sequence of real numbers with (equation omitted). A central limit theorem for a stationary linear process generated by stationary associated processes is also discussed.