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Teoriya Veroyatnostei i ee Primeneniya, 2002, Volume 47, Issue 4, Pages 769–772
DOI: https://doi.org/10.4213/tvp3780 (Mi tvp3780) 		 
Short Communications

A nonuniform estimate for the error in short asymptotic expansions in Hilbert space

S. A. Bogatyrev

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (458 kB)
DOI: https://doi.org/10.4213/tvp3780
Abstract: This work considers short asymptotic expansions of the probability for a sum of independent random elements to hit a ball in Hilbert space. An estimate for the error of the decomposition which is optimal with respect to a number of summands and depending only on at most 12 eigenvalues of the covariance operator of a summand is obtained. The error decreases if the distance between the bound of the ball and the zero element increases.
Keywords: short asymptotic expansions, Hilbert space, nonuniform estimate.
Received: 19.08.2002
English version:
Theory of Probability and its Applications, 2003, Volume 47, Issue 4, Pages 689–692
DOI: https://doi.org/10.1137/S0040585X97980063
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. A. Bogatyrev, “A nonuniform estimate for the error in short asymptotic expansions in Hilbert space”, Teor. Veroyatnost. i Primenen., 47:4 (2002), 769–772; Theory Probab. Appl., 47:4 (2003), 689–692
Citation in format AMSBIB
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