Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 39-50
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Let $n$ balls be distributed at random in $N$ boxes. Each ball may fall into any box with the same probability $1/N$ independently of the others. Let $\mu_r(n)$ be the number of boxes which contain exactly $r$ balls $(r=1,2,\dots)$. We consider $\mu_r(n)$ as a random function of the time parameter $n$. In this paper we prove that the random function $\mu_r(n)$ converges to some Gaussian or Poisson process as $n$, $N\to\infty$.
@article{TVP_1968_13_1_a2,
author = {Yu. V. Bolotnikov},
title = {Convergence of the variables $\mu_r(n)$ to {Gaussian} and {Poisson} processes in the classical problem with balls},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {39--50},
publisher = {mathdoc},
volume = {13},
number = {1},
year = {1968},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/}
}
TY - JOUR AU - Yu. V. Bolotnikov TI - Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1968 SP - 39 EP - 50 VL - 13 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/ LA - ru ID - TVP_1968_13_1_a2 ER -
%0 Journal Article %A Yu. V. Bolotnikov %T Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls %J Teoriâ veroâtnostej i ee primeneniâ %D 1968 %P 39-50 %V 13 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/ %G ru %F TVP_1968_13_1_a2
Yu. V. Bolotnikov. Convergence of the variables $\mu_r(n)$ to Gaussian and Poisson processes in the classical problem with balls. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 1, pp. 39-50. http://geodesic.mathdoc.fr/item/TVP_1968_13_1_a2/