• 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 Mathematical Society
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• v.36 no.4
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• pp.737-746
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• 1999

We consider a class of discrete parameter processes on a locally compact Banach space S arising from successive compositions of strictly stationary random maps with state space C(S,S), where C(S,S) is the collection of continuous functions on S into itself. Sufficient conditions for stationary solutions are found. Existence of pth moments and convergence of empirical distributions for trajectories are proved.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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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).

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.153-158
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• 2001

A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.485-490
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• 1998

We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.117-123
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• 2005

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.95-102
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• 2002

A central limit theorem is obtained for a stationary multivariate linear process of the form (equation omitted), where { $Z_{t}$} is a sequence of strictly stationary m-dimensional associated random vectors with E $Z_{t}$ = O and E∥ $Z_{t}$∥$^2$ < $\infty$ and { $A_{u}$} is a sequence of coefficient matrices with (equation omitted) and (equation omitted).ted)..ted).).

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.309-319
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• 2002

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.119-121
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• 2000

A functional central limit theorem is obtained for a stationary multivariate linear process of the form $X_t=\sum\limits_{u=0}^\infty{A}_{u}Z_{t-u}$, where {$Z_t$} is a sequence of strictly stationary m-dimensional linearly positive quadrant dependent random vectors with $E Z_t = 0$ and $E{\parallel}Z_t{\parallel}^2 <{\infty}$ and {$A_u$} is a sequence of coefficient matrices with $\sum\limits_{u=0}^\infty{\parallel}A_u{\parallel}<{\infty}$ and $\sum\limits_{u=0}^\infty{A}_u{\neq}0_{m{\times}m}$. AMS 2000 subject classifications : 60F17, 60G10.