On the local limit theorem for critical Galton–Watson process
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 457-479 Cet article a éte moissonné depuis la source Math-Net.Ru

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The proof of the local limit theorem for a critical Galton–Watson process is given under minimal moment restrictions, i.e., under the condition that there exists the second moment of the number of direct offspring of one particle.
Keywords: Galton–Watson process, Bellman–Harris process, concentration function, local theorem, bilinear generating function.
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S. V. Nagaev; V. I. Vakhtel'. On the local limit theorem for critical Galton–Watson process. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 457-479. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a2/

[1] Zolotarev V. M., “Utochnenie ryada teorem teorii vetvyaschikhsya sluchainykh protsessov”, Teoriya veroyatn. i ee primen., 2:2 (1957), 256–266 | MR | Zbl

[2] Kesten H., Ney P., Spitzer F., “The Galton–Watson process with mean one and finite variance”, Teoriya veroyatn. i ee primen., 11:4 (1966), 579–611 | MR | Zbl

[3] Vatutin V. A., “Lokalnaya predelnaya teorema dlya kriticheskikh vetvyaschikhsya protsessov Bellmana–Kharrisa”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 158, 1981, 9–30 | MR | Zbl

[4] Chistyakov V. P., “Lokalnye predelnye teoremy teorii vetvyaschikhsya sluchainykh protsessov”, Teoriya veroyatn. i ee primen., 2:3 (1957), 360–374 | MR | Zbl

[5] Athreya K. B., Ney P., Branching Processes, Springer-Verlag, New York, Heidelberg, 1972, 287 pp. | MR | Zbl

[6] Nagaev S. V., Mukhamedkhanova R., “Nekotorye predelnye teoremy iz teorii vetvyaschikhsya protsessov”, Predelnye teoremy i statisticheskie vyvody, Fan, Tashkent, 1966, 90–112 | MR

[7] Topchii V. A., “Lokalnaya predelnaya teorema dlya kriticheskikh protsessov Bellmana–Kharrisa s diskretnym vremenem”, Predelnye teoremy teorii veroyatnostei i smezhnye voprosy, Trudy In-ta matematiki, 1, Nauka, Novosibirsk, 1982, 97–122 | MR

[8] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972, 414 pp. | MR

[9] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967, 376 pp. | MR

[10] Nagaev S. V., “Otsenka pogreshnosti priblizheniya ustoichivymi zakonami. I”, Teoriya imov. i matem. statist., 55 (1997), 145–160 | MR

[11] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1967, 498 pp. | MR