RUS  ENG
Full version
JOURNALS // Diskretnaya Matematika
Diskr. Mat., 2000, Volume 12, Issue 1, Pages 7–23 (Mi dm324)
Convergence conditions for weighted branching processes
U. Rösler, V. A. Topchii, V. A. Vatutin

References
1. Athreya K. B., Ney P., Branching Processes, Springer, New York, 1972  mathscinet  zmath
2. Asmussen S., Hering H., Branching Processes, Birkhäuser, Boston, 1983  mathscinet  zmath
3. Biggins J. D., “Martingale convergence in the branching random walk”, J. Appl. Probab., 14:1 (1997), 25–37  crossref  mathscinet
4. Biggins J. D., Kyprianou A. E., “Seneta–Heyde norming in the branching random walk”, Ann. Probab, 25:1 (1977), 337–360  mathscinet
5. Blackwell D, Dubins L. E., “A converse to the dominated convergence theorem”, Illinois J. Math., 7 (1963), 508–514  mathscinet  zmath
6. Cramer M., Rüschendorf L., “Convergence of a branching type recursion”, Annales de l'Institut Henri Poincaré. Probabilités et Statistiques, 32 (1996), 725–741  mathscinet  zmath
7. Davies L., “A theorem of Deny with applications to characterization problems”, Lect. Notes Math., 861, 1981, 35–41  mathscinet  zmath
8. Davies L., Shimizu R., “On identically distributed linear statistics”, Ann. Inst. Statist. Math., 28 (1976), 469–489  crossref  mathscinet  zmath
9. Dub Dzh. L., Veroyatnostnye protsessy, IL, Moskva, 1956
10. Durrett R., Liggett M., “Fixed points of the smoothing transformation”, Z. Wahrsch. Verw. Gebiete, 64 (1983), 275–301  crossref  mathscinet  zmath
11. Lindenstrauss J., Tzafriri L., Classical Banach Spaces, v. 1–2, Springer, Berlin, 1977–79  mathscinet
12. Liu Q., “Sur une équation fonctionnelle et ses applications: une extension du théorème de Kesten–Stigum concernant des processus de branchement”, Adv. Appl. Probab., 29 (1977), 353–373  crossref  mathscinet
13. Lyons R., “A simple path to Biggins' martingale convergence”, Classical and Modern Branching Processes, 1996, 217–222, Springer, Berlin  mathscinet
14. Rösler U., “A fixed point theorem for distributions”, Stoch. Proc. and their Appl., 42:2 (1992), 195–214  mathscinet  zmath
15. Rösler U., “The weighted branching process”, Dynamics of complex and irregular systems, Bielefeld Encount. Math. Phys., VIII, World Science Publishing, River Edge, 1993, 154–165  mathscinet
16. Rösler U., “A fixed point equation for distributions”, Berichtsreihe des Mathematischen Seminars Kiel, 1998, 98–7
17. U. Rösler, L. Rüschendorf, “The contraction method for recursive algorithms”, Algorithmica, 29:1-2 (2001), 3–33  mathscinet
18. Shimizu R., “Solutions to a functional equation and its applications to some characterization problems”, Shankhya, Ser. A, 40 (1978)  mathscinet  zmath
19. Vatutin V. A., Topchii V. A., “Maksimum kriticheskikh protsessov Galtona–Vatsona i nepreryvnye sleva sluchainye bluzhdaniya”, Teoriya veroyatnostei i ee primeneniya, 42 (1997), 21–34  mathnet  mathscinet  zmath
20. Krasnoselskii M. A., Rutskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, Fizmatgiz, Moskva, 1958
21. Meier P. A., Veroyatnost i potentsialy, Mir, Moskva, 1973
22. Shiryaev A. N., Veroyatnost, Nauka, Moskva, 1989  mathscinet
23. Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, Gostekhizdat, Moskva, 1948

© Steklov Math. Inst. of RAS, 2026