Geodesic
On limit theorem for the number of vertices of the convex hulls in a unit disk
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 275-284

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to further investigation of the property of a number of vertices of convex hulls generated by independent observations of a two-dimensional random vector with regular distributions near the boundary of support when it is a unit disk. Following P. Groeneboom [4], the Binomial point process is approximated by the Poisson point process near the boundary of support and vertex processes of convex hulls are constructed. The properties of strong mixing and martingality of vertex processes are investigated. Using these properties, asymptotic expressions are obtained for the expectations and variance of the vertex processes that correspond to the results previously obtained by H. Carnal [2]. Further, using the properties of strong mixing of vertex processes, the central limit theorem for a number of vertices of a convex hull is proved.
Keywords: convex hull, Markovian jump process, Central limit theorem.
Mots-clés : Poisson point process, martingales 
@article{JSFU_2020_13_3_a1,
     author = {Isakjan M. Khamdamov},
     title = {On limit theorem for the number of vertices of the convex hulls in a unit disk},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {275--284},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a1/}
}
TY  - JOUR
AU  - Isakjan M. Khamdamov
TI  - On limit theorem for the number of vertices of the convex hulls in a unit disk
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 275
EP  - 284
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a1/
LA  - en
ID  - JSFU_2020_13_3_a1
ER  - 
%0 Journal Article
%A Isakjan M. Khamdamov
%T On limit theorem for the number of vertices of the convex hulls in a unit disk
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 275-284
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a1/
%G en
%F JSFU_2020_13_3_a1
Isakjan M. Khamdamov. On limit theorem for the number of vertices of the convex hulls in a unit disk. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 275-284. http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a1/