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On a functional central limit theorem for the linear process generated by associated random variables in a Hilbert space

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Let {수식} be a strictly stationary associated sequence of H-valued random variables with [수식] and [수식] and {수식} a sequence of linear operators such that [수식]. For a linear process [수식] we derive that {Xk} fulfills the functional central limit theorem.

Abstract

Let {수식} be a strictly stationary associated sequence of H-valued random variables with [수식] and [수식] and {수식} a sequence of linear operators such that [수식]. For a linear process [수식] we derive that {Xk} fulfills the functional central limit theorem.

참고문헌 (12)

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  5. P. Brockwell, "Time Series, Theory and Method" (1987), Springer
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  9. Tae-Sung Kim, "A central limit theorem for the stationary multivariate linear process generated by associated random vectors", 대한수학회논문집, 17(1), pp.95~102 (2002), 대한수학회
  10. Tae-Sung Kim, "On a functional central limit theorem for stationary linear processes generated by associated processes", 대한수학회지, 40(4), pp.715~722 (2003), 대한수학회
  11. C. M. Newman, "Normal fluctuations and the FKG inequalities", Comm. Math. Phys, 74, pp.119~128 (1980)
  12. C. M. Newman, "An invariance principle for certain dependent sequences", Ann. Probab, 9, pp.671~675 (1981)

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