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

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

[发布日期] 1996-12-13

[关键词] Hilbertian white noise;Hilbert space valued linear processes;central limit theorem;uniform integrability