• 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 Data and Information Science Society
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• v.16 no.2
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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 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.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.219-224
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• 1995

A central limit theorem with random indices is obtained for stattionary martingale difference sequences.

• 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.28 no.3
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• pp.571-580
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• 2013

In this paper, we extend the familiar limit curve theorem in [2] to a situation where each causal curve lies in a sequence of compact interpolating spacetimes converging to a limit Lorentz space in the sense of Lorentzian Gromov-Hausdorff distance.

• 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 for Statistical Applications and Methods
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• v.16 no.4
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• pp.687-696
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• 2009

We prove a central limit theorem for the negatively associated random variables in a Hilbert space and extend this result to the linear process generated by negatively associated random variables in a Hilbert space. Our result implies an extension of the central limit theorem for the linear process in a real space under negative association to a simplest case of infinite dimensional Hilbert space.

• Journal of the Korean Mathematical Society
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• v.37 no.3
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• pp.463-471
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• 2000

A central limit theorem is obtained for stationary linear process Xt = aj$\varepsilon$t-j, where {$\varepsilon$t} a strictly stationary associated sequence with Et < and {aj} is a sequence of real numbers with <. A functional central limit theorem is also derived.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.88-93
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• 1982

A local limit theorem for large deviations for the i.i.d. random variables was given by Richter (1957), who used the saddle point method of complex variables to prove it. In this paper we give an alternative form of local limit theorem for large deviations for the i.i.d. random variables which is essentially equivalent to that of Richter. We prove the theorem by more direct and heuristic method under a rather simple condition on the moment generating function (m.g.f.). The theorem is proved without assuming that $E(X_i)=0$.