Geodesic
Two sequential test schemes with aftereffect
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 89-96.

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

Two variants of the urn scheme with aftereffect are described. Using $\mathrm{A}$- and $\Phi$-schemes of sequential tests, we find an explicit distribution of the number of removed balls of a certain color, obtain numerical characteristics of the distribution, and prove limit theorems.
Keywords: urn scheme, $\mathrm{A}$-scheme of sequential tests, $\Phi$-scheme of sequential tests, probability, limit theorem.
Mots-clés : distribution 
@article{INTO_2023_224_a10,
     author = {N. A. Kolokol'nikova},
     title = {Two sequential test schemes with aftereffect},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {89--96},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a10/}
}
TY  - JOUR
AU  - N. A. Kolokol'nikova
TI  - Two sequential test schemes with aftereffect
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 89
EP  - 96
VL  - 224
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_224_a10/
LA  - ru
ID  - INTO_2023_224_a10
ER  - 
%0 Journal Article
%A N. A. Kolokol'nikova
%T Two sequential test schemes with aftereffect
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 89-96
%V 224
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_224_a10/
%G ru
%F INTO_2023_224_a10
N. A. Kolokol'nikova. Two sequential test schemes with aftereffect. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 89-96. http://geodesic.mathdoc.fr/item/INTO_2023_224_a10/

[1] Dokin V. N., Zhukov V. D., Kolokolnikova N. A., Kuzmin O. V., Platonov M. L., Kombinatornye chisla i polinomy v modelyakh diskretnykh raspredelenii, Izd-vo Irkut. un-ta, Irkutsk, 1990 | MR

[2] Ivchenko G. I., Medvedev Yu. A., “Protsess posledovatelnogo zapolneniya yacheek v skheme razmescheniya chastits kak markovskaya tsep”, Obozr. prikl. prom. mat., 3:4 (1996), 512–529 | Zbl

[3] Ivchenko G. I., Medvedev Yu. A., “Issledovanie protsessa zapolneniya yacheek v skheme razmescheniya s otrazheniem”, Diskr. mat., 6:1 (1994), 40–52 | Zbl

[4] Ivchenko G. I., Medvedev Yu. I., “Ob urnovoi skheme Markova—Poia: ot 1917 g. do nashikh dnei”, Obozr. prikl. prom. mat., 3:4 (1996), 484–511 | Zbl

[5] Imykhelova V. P., Kolokolnikova N. A., “Odna skhema sluchainogo razmescheniya chastits («skolzyaschii komplekt»)”, Asimptoticheskie i perechislitelnye zadachi kombinatornogo analiza, Izd-vo Irkut. un-ta, Irkutsk, 1997, 43–53

[6] Kolokolnikova N. A., Kotomanova D. V., “A-skhema posledovatelnykh ispytanii i sluchainye razmescheniya s otrazheniem”, Trudy IMEI IGU. Matematika i informatika. T. 1, Izd-vo Irkut. un-ta, Irkutsk, 2011, 69–72

[7] Kolokolnikova N. A., “Veroyatnostnye modeli teorii strakhovaniya, ispolzuyuschie skhemy sluchainogo razmescheniya chastits”, Informatsionnye tekhnologii i problemy matematicheskogo modelirovaniya slozhnykh sistem, v. 15, Izd-vo IrGUPS, Irkutsk, 2015, 59–65

[8] Kolokolnikova N. A., “Odno obobschenie urnovoi skhemy Markova—Poia”, Prikladnye problemy diskretnogo analiza, Izd-vo Irkut. un-ta, Irkutsk, 2021, 59–65

[9] Kolokolnikova N. A., Predelnye teoremy dlya chisla uspekhov v odnoi skheme zavisimykh ispytanii. Dep. No 649. V92, VINITI RAN, M., 1992

[10] Kolchin V. F., Sevastyanov B. A., Chistyakov V. P., Sluchainye razmescheniya, Nauka, M., 1975 | MR

[11] Markov A. A., “O nekotorykh predelnykh formakh ischisleniya veroyatnostei”, Izv. AN., 11:3 (1917), 177–186

[12] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978 | MR

[13] Sevastyanov B. A., “Ob odnoi skheme zavisimykh razmeschenii”, Izv. AN UzSSR. Ser. fiz.-mat., 1981, no. 2, 37–41 | Zbl

[14] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya. T. 1, Mir, M., 1984 | MR

[15] Bender E. A., “Central and local limit theorems applied to asimptotic enumeration”, J. Comb. Theory., 15:1 (1973), 91–111 | DOI | MR | Zbl