Rates of convergence in the CLT for linear random fields

被引：0
作者：
Edgaras Mielkaitis
Vygantas Paulauskas
机构：
[1] Vilnius University,Faculty of Mathematics and Informatics
[2] Vilnius University,Institute of Mathematics and Informatics
来源：
Lithuanian Mathematical Journal | 2011年 / 51卷
关键词：
central limit theorem; linear random fields; rate of convergence; 60F05; 60B12;
D O I：
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学科分类号：
摘要：
In this paper, we study sums of linear random fields defined on the lattice Z2 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−p 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, 2002 (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, 2004] for linear processes.
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页码：233 / 250
页数：17
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