Abstract
The central limit theorem is proved for linear random fields defined on an integer-valued lattice of arbitrary dimension and taking values in Hilbert space. It is shown that the conditions in the central limit theorem are optimal.
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Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 421–428, September, 2000.
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Nazarova, A.N. Normal approximation for linear stochastic processes and random fields in Hilbert space. Math Notes 68, 363–369 (2000). https://doi.org/10.1007/BF02674560
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DOI: https://doi.org/10.1007/BF02674560