Geodesic
Multidimensional records of particle scores in overcritical branching processes with continuous time
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2022), pp. 14-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Bivariate records of particle scores in immortal supercritical branching processes with continuous time are studied. The limiting intensity of records for one score and the limiting intensity of records for both scores or at least one score are found. In the case of independent scores, mean numbers of joint records for all time are calculated. The results are illustrated by examples. 
@article{VMUMM_2022_6_a2,
     author = {A. V. Nazmutdinova},
     title = {Multidimensional records of particle scores in overcritical branching processes with continuous time},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--20},
     year = {2022},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a2/}
}
TY  - JOUR
AU  - A. V. Nazmutdinova
TI  - Multidimensional records of particle scores in overcritical branching processes with continuous time
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2022
SP  - 14
EP  - 20
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a2/
LA  - ru
ID  - VMUMM_2022_6_a2
ER  - 
%0 Journal Article
%A A. V. Nazmutdinova
%T Multidimensional records of particle scores in overcritical branching processes with continuous time
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2022
%P 14-20
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a2/
%G ru
%F VMUMM_2022_6_a2
A. V. Nazmutdinova. Multidimensional records of particle scores in overcritical branching processes with continuous time. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2022), pp. 14-20. http://geodesic.mathdoc.fr/item/VMUMM_2022_6_a2/

[1] Arnold B. C., Villasenor J. A., “The tallest man in the world”, Statist. Theory and Appl., Papers in Honor of H.A. David, Springer, N. Y., 1996, 81–88 | MR

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

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

[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] Nevzorov V. B., Rekordy. Matematicheskaya teoriya, Fazis, M., 2000 | MR

[7] Hashorva E., Hüsler J., “Multiple maxima in multivariate samples”, Statist. and Probab. Letters, 75 (2005), 11–17 | DOI | MR

[8] Dombry C., Zott M., “Multivariate records and hitting scenarios”, Extremes, 21 (2018), 343–361 | DOI | MR

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

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

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

[12] Karpenko A. V., “Novye svoistva dvumernykh maksimumov priznakov chastits v vetvyaschikhsya protsessakh s nepreryvnym vremenem”, Vestn. Mosk. un-ta. Matem. Mekhan., 2020, no. 1, 17–23

[13] Karpenko A. V., “Svoistva dvumernykh maksimumov priznakov chastits v kriticheskikh vetvyaschikhsya protsessakh s immigratsiei i nepreryvnym vremenem”, Matem. zametki, 109:2 (2021), 235–246

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

[15] Ghoudi K., Khoudraji A., Rivest L., “Proprietes statistiques des copules de valeurs extremes bidimensionnelles”, Can. J. Statist., 26:1 (1998), 189–190 | DOI | MR

[16] Weisstein E. W., Polygamma Function, https://mathworld.wolfram.com/PolygammaFunction.html