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

Florence Merlevède

Stochastic Processes and their Applications, 1996, vol. 65, issue 1, 103-114

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.

Keywords: 60F05; 60G50; Hilbertian; white; noise; Hilbert; space; valued; linear; processes; central; limit; theorem; Uniform; integrability (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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