Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 182-187
Citer cet article
V. G. Mikhailov. Limit distributions of random variables connected with multiple long duplications in a sequence lof independent trials. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 182-187. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/
@article{TVP_1974_19_1_a17,
author = {V. G. Mikhailov},
title = {Limit distributions of random variables connected with multiple long duplications in a~sequence lof independent trials},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {182--187},
year = {1974},
volume = {19},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/}
}
TY - JOUR
AU - V. G. Mikhailov
TI - Limit distributions of random variables connected with multiple long duplications in a sequence lof independent trials
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1974
SP - 182
EP - 187
VL - 19
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/
LA - ru
ID - TVP_1974_19_1_a17
ER -
%0 Journal Article
%A V. G. Mikhailov
%T Limit distributions of random variables connected with multiple long duplications in a sequence lof independent trials
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1974
%P 182-187
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a17/
%G ru
%F TVP_1974_19_1_a17
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 multiple long duplications \begin{gather*} ((X_{i_1}, X_{i_1+1},\dots,X_{i_1+n-1})=(X_{i_t}, X_{i_t+1},\dots,X_{i_t+n-1}) \\ t=2,\dots,k,\quad1\le i_1<\dots<i_k\le N), \end{gather*} for the distribution of the waiting time until the first multiple duplication of a given length and for the distribution of the maximal duplication length.
