Rates of convergence in the CLT for linear random fields.

In this paper, we study sums of linear random fields defined on the lattice Z with values in a Hilbert space. The rate of convergence of distributions of such sums to the Gaussian law is discussed, and mild sufficient conditions to obtain an approximation of order n are presented. This can be considered as a complement of a recent result of [A.N. Nazarova, Logarithmic velocity of convergence in CLT for stochastic linear processes and fields in a Hilbert space, Fundam. Prikl. Mat., 8:1091-1098, (in Russian)], where the logarithmic rate of convergence was stated, and as a generalization of the result of [D. Bosq, Erratum and complements to Berry-Esseen inequality for linear processes in Hilbert spaces, Stat. Probab. Lett., 70:171-174, ] for linear processes. [ABSTRACT FROM AUTHOR]