Marcinkiewicz–Zygmund laws for Banach space valued random variables with multidimensional parameters
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 213-219
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For finite-dimensional array $X(m)=X(m_1,\dots,m_k)$ of independent identically distributed Banach space valued random variables we consider sums $S(n)=S(n_1,\dots,n_k)$ of $X(m)$ over $m_i\in\{1,\dots,n_i\}$ $(i-1,\dots,k)$. Under some conditions on individual random variable $X$ and on the geometry of Banach space the strong law of large numbers for $S(n)$ and estimates for large deviations as $\max n_i\to\infty$ are obtained.
Keywords:
Banach space valued random Variables, law of large numbers for multidimensional sums, large deviation probabilities.
Nguyen Van Giang. Marcinkiewicz–Zygmund laws for Banach space valued random variables with multidimensional parameters. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 213-219. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a18/
@article{TVP_1995_40_1_a18,
author = {Nguyen Van Giang},
title = {Marcinkiewicz{\textendash}Zygmund laws for {Banach} space valued random variables with multidimensional parameters},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {213--219},
year = {1995},
volume = {40},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a18/}
}
TY - JOUR AU - Nguyen Van Giang TI - Marcinkiewicz–Zygmund laws for Banach space valued random variables with multidimensional parameters JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1995 SP - 213 EP - 219 VL - 40 IS - 1 UR - http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a18/ LA - en ID - TVP_1995_40_1_a18 ER -