Geodesic
New properties of bivariate maxima of particle scores in branching processes with continuous time
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 17-23 
A. V. Karpenko. New properties of bivariate maxima of particle scores in branching processes with continuous time. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 17-23. http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a1/
@article{VMUMM_2020_1_a1,
     author = {A. V. Karpenko},
     title = {New properties of bivariate maxima of particle scores in branching processes with continuous time},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {17--23},
     year = {2020},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a1/}
}
TY  - JOUR
AU  - A. V. Karpenko
TI  - New properties of bivariate maxima of particle scores in branching processes with continuous time
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2020
SP  - 17
EP  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a1/
LA  - ru
ID  - VMUMM_2020_1_a1
ER  - 
%0 Journal Article
%A A. V. Karpenko
%T New properties of bivariate maxima of particle scores in branching processes with continuous time
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2020
%P 17-23
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a1/
%G ru
%F VMUMM_2020_1_a1

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

Bivariate maxima of particle scores in immortal branching processes with continuous time are studied. The limit distribution for a maximum of two scores at two points in time is found. The limit intensities of the up and down jumps of the maximum for both sбores or at least one score are obtained. In the case of independent scores, mean total numbers of joint maxima jumps up and down are calculated. Results are illustrated by examples.

[1] Arnold B. C., Villasenor J. A., “The tallest man in the world”, Statistical theory and applications, Papers in honor of H. A. David, Springer, N.Y., 1996, 81–88 | DOI | MR | Zbl

[2] Pakes A. G., “Extreme order statistics on Galton–Watson trees”, Metrika, 47:1 (1998), 95–117 | DOI | MR | Zbl

[3] Vatutin V. A., Vetvyaschiesya protsessy i ikh primeneniya, Lektsionnye kursy NOTs, 8, Matem. in-t RAN, M., 2008 | DOI

[4] Kharris T., Teoriya vetvyaschikhsya sluchainykh protsessov, Mir, M., 1966

[5] Mitov K. V., Yanev G. P., “Maximum individual score in critical two-type branching processes”, C. r. Acad. Bulg. Sci., 55:11 (2002), 7–22 | MR

[6] Lebedev A. V., “Maxima of random particles scores in Markov branching processes with continuous time”, Extremes, 11:2 (2008), 203–216 | DOI | MR | Zbl

[7] Lebedev A. V., Neklassicheskie zadachi stokhasticheskoi teorii ekstremumov, Dokt. dis., M., 2016

[8] Lebedev A. V., “Mnogomernye ekstremumy sluchainykh priznakov chastits v vetvyaschikhsya protsessakh s maksimum-lineinoi nasledstvennostyu”, Matem. zametki, 105:3 (2019), 395–405 | DOI | MR | Zbl

[9] Nelsen R., An Introduction to Copulas, Springer, N. Y., 2006 | MR | Zbl