Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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FUNCTIONAL CENTRAL LIMIT THEOREMS FOR MULTIVARIATE LINEAR PROCESSES GENERATED BY DEPENDENT RANDOM VECTORS

  • Ko, Mi-Hwa (Department of Mathematics WonKwang University)
  • Published : 2006.10.31
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Abstract

Let $\mathbb{X}_t$ be an m-dimensional linear process defined by $\mathbb{X}_t=\sum{_{j=0}^\infty}\;A_j\;\mathbb{Z}_{t-j}$, t = 1, 2, $\ldots$, where $\mathbb{Z}_t$ is a sequence of m-dimensional random vectors with mean 0 : $m\times1$ and positive definite covariance matrix $\Gamma:m{\times}m$ and $\{A_j\}$ is a sequence of coefficient matrices. In this paper we give sufficient conditions so that $\sum{_{t=1}^{[ns]}\mathbb{X}_t$ (properly normalized) converges weakly to Wiener measure if the corresponding result for $\sum{_{t=1}^{[ns]}\mathbb{Z}_t$ is true.

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References

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  1. A Central Limit Theorem for the Linear Process in a Hilbert Space under Negative Association vol.16, pp.4, 2009, https://doi.org/10.5351/CKSS.2009.16.4.687