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ON FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LINEAR RANDOM FIELDS WITH DEPENDENT INNOVATIONS

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 April 2008

MI-HWA KO ,
HYUN-CHULL KIM  and
TAE-SUNG KIM
MI-HWA KO
Affiliation:
Department of Mathematics, WonKwang University, Jeonbuk, 570-749, Korea (email: [email protected])
HYUN-CHULL KIM
Affiliation:
Department of Mathematics Education, Daebul University, 526-720, Korea (email: [email protected])
TAE-SUNG KIM*
Affiliation:
Department of Mathematics, WonKwang University, Jeonbuk, 570-749, Korea (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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For a linear random field (linear p-parameter stochastic process) generated by a dependent random field with zero mean and finite qth moments (q>2p), we give sufficient conditions that the linear random field converges weakly to a multiparameter standard Brownian motion if the corresponding dependent random field does so.

Keywords

functional central limit theoremrandom fieldassociatedlinear random fieldsmartingale differencedecomposition

MSC classification

Secondary: 60F17: Functional limit theorems; invariance principles 60G15: Gaussian processes
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 533 - 541
Copyright
Copyright © Australian Mathematical Society 2008

References

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