Geodesic
A nonuniform estimate for the error in short asymptotic expansions in Hilbert space
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 769-772

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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. 
@article{TVP_2002_47_4_a8,
     author = {S. A. Bogatyrev},
     title = {A nonuniform estimate for the error in short asymptotic expansions in {Hilbert} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {769--772},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a8/}
}
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S. A. Bogatyrev. A nonuniform estimate for the error in short asymptotic expansions in Hilbert space. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 769-772. http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a8/