Abstract
In the present study we consider a normal separable stochastic continuous field, and we prove the convergence of a Karhunen series with probability 1 for all parameter values. This leads in particular, to the nonrandomness of points of the discontinuity and values of the discontinuity. A criterion is presented for the convergence of the canonical expansion in a uniform norm.
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Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 565–572, October, 1973.
The author thanks S. A. Molchanov for guidance with the work and Yu. K. Belayev for help and valuable instruction.
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Ostrovskii, E.I. Convergence of a canonical expansion for normal fields. Mathematical Notes of the Academy of Sciences of the USSR 14, 881–885 (1973). https://doi.org/10.1007/BF01108819
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DOI: https://doi.org/10.1007/BF01108819