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
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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
$$
((X_i,X_{i+1},\dots,X_{i+n-1})=(X_j,X_{j+1},\dots,X_{j+n-1}),\quad1\le i\le N),
$$
for the distribution of the waiting time until the first duplication of a given length and for the distribution of the maximal duplication length.
@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},
publisher = {mathdoc},
volume = {19},
number = {1},
year = {1974},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a16/ %G ru %F TVP_1974_19_1_a16
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/