Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 173-181
Citer cet article
A. M. Zubkov; V. G. Mikhailov. Limit distributions of random variables connected with long duplications in a sequence of independent trials. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 173-181. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a16/
@article{TVP_1974_19_1_a16,
author = {A. M. Zubkov and V. G. Mikhailov},
title = {Limit distributions of random variables connected with long duplications in a~sequence of independent trials},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {173--181},
year = {1974},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a16/}
}
TY - JOUR
AU - A. M. Zubkov
AU - V. G. Mikhailov
TI - Limit distributions of random variables connected with long duplications in a sequence of independent trials
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 173
EP - 181
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a16/
LA - ru
ID - TVP_1974_19_1_a16
ER -
%0 Journal Article
%A A. M. Zubkov
%A V. G. Mikhailov
%T Limit distributions of random variables connected with long duplications in a sequence of independent trials
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 173-181
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a16/
%G ru
%F TVP_1974_19_1_a16
Let $X_0,X_1,\dots$ be a sequence of independent trials with $m$ outcomes. We prove limit theorems for the distribution of the number of long duplications $$ ((X_i,X_{i+1},\dots,X_{i+n-1})=(X_j,X_{j+1},\dots,X_{j+n-1}),\quad1\le i<j\le N), $$ for the distribution of the waiting time until the first duplication of a given length and for the distribution of the maximal duplication length.
