# ON A FUNCTIONAL CENTRAL LIMIT THEOREM FOR STATIONARY LINEAR PROCESSES GENERATED BY ASSOCIATED PROCESSES

• Kim, Tae-Sung (Division of Mathematics and Informational Statistics and Institute of Basic Natural Science, Wonkwang University) ;
• Ko, Mi-Hwa (Division of Mathematics and Informational Statistics and Institute of Basic Natural Science, Wonkwang University)
• Published : 2003.11.01

#### Abstract

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.

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#### Cited by

1. A central limit theorem for the linear process generated by associated random variables in a Hilbert space vol.78, pp.14, 2008, https://doi.org/10.1016/j.spl.2008.01.079