대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제21권4호
  • /
  • Pages.779-786
  • /
  • 2006
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

FUNCTIONAL CENTRAL LIMIT THEOREMS FOR MULTIVARIATE LINEAR PROCESSES GENERATED BY DEPENDENT RANDOM VECTORS

  • Ko, Mi-Hwa (Department of Mathematics WonKwang University)
  • 발행 : 2006.10.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. D. J. Aldous and G. K. Eagleson, On mixing and stability of limit theorems, Ann. Probability. 6 (1978), 325-331 https://doi.org/10.1214/aop/1176995577
  2. G. J. Babu and M. Ghosh, A ranldom functional central limit theorem for martingales, Acta. Math. Scie. Hungar. 27 (1976), 301-306 https://doi.org/10.1007/BF01902107
  3. P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968
  4. P. J. Brockwell and R. A. Davis, Time Series: Theory and Methods 2nd ed., Springer, New York, 1987
  5. R. M. Burton, A. R. Darbrowski, and H. Dehling, An invariance principle for weakly associated random vectors, Stoc. Proc. and Appl. 23 (1986), 301-306 https://doi.org/10.1016/0304-4149(86)90043-8
  6. I. Fakhre-Zakeri and S. Lee, On functional centmllimit theorems for multivariate linear processes with applications to sequential estimation, J. Stat. Plan. Inf. 3 (2000), 11-23
  7. W. A. Fuller, Introduction to Statistical Time-Series, 2nd Edition. Wiley Inc, New York, 1996
  8. T. S. Kim, Y. K. Choi, and M. H. Ko, The random functional central limit theorem for multivariate martingale difference, Taiwanese J. Math. accepted, (2006)
  9. C. M. Newman, Asymptotic independence and limit theorems for positively and negatively dependent random variables, in: Tong, Y.L., ed., IMS Lecture Notes-Monograph series. 5 (1984), 127-140
  10. D. Pollard, Convergence of Stochastic Processes, Wiley, New York, 1984
  11. Q. M. Shao, A comparison theorem on maximum inequalities between negatively associated and independent random variables, J. Theor. Probab. 13 (2000), 343-356 https://doi.org/10.1023/A:1007849609234

피인용 문헌

  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