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Central limit theorem for linear processes with values in a Hilbert space

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  • Merlevède, Florence

Abstract

In this paper we study the behavior of Sn = [summation operator]nk = 1[alpha]nk[var epsilon]k associated to an i.i.d. sequence ([var epsilon]k, k [set membership, variant] Z) with values in a real separable Hilbert space H of infinite dimension, and where ([alpha]nk, 1 [less-than-or-equals, slant] k [less-than-or-equals, slant] n) is a triangular array of bounded linear operators from H to H. We shall provide sufficient conditions for the CLT for (Sn, n [greater-or-equal, slanted] 1) imposed on the norm of the operators and on the moments of Sn.

Suggested Citation

  • Merlevède, Florence, 1996. "Central limit theorem for linear processes with values in a Hilbert space," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 103-114, December.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:103-114
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    Cited by:

    1. Besnik Pumo, 1998. "Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 297-309, October.

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