Precise Laplace-type asymptotics for moderate deviations
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 720-744
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Formulas are deduced allowing one to find precise asymptotics of
moderate deviations for the distributions of sums of independent
identically distributed Banach-valued random elements. This
result is proved by the Laplace method in Banach spaces. This
method is an extension of the classical asymptotic Laplace method
to the case of integrals with respect to probability measures in
infinite-dimensional Banach spaces. By means of the theorem
established in the present paper we find asymptotic
representations for the probabilities of moderate deviations of
statistics of the form $\omega_n^p$, $p\ge 2$.
Keywords:
sums of independent random elements, Laplace method in Banach spaces, action functional, Cramér transform, probabilities of moderate deviations of statistics of the form $\omega_n^p$.
@article{TVP_2003_48_4_a4,
author = {V. R. Fatalov},
title = {Precise {Laplace-type} asymptotics for moderate deviations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {720--744},
publisher = {mathdoc},
volume = {48},
number = {4},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a4/}
}
V. R. Fatalov. Precise Laplace-type asymptotics for moderate deviations. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 720-744. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a4/