Multitype Galton–Watson branching processes in Markovian random environment
Teoriâ veroâtnostej i ee primeneniâ, Tome 56 (2011) no. 3, pp. 592-601 Cet article a éte moissonné depuis la source Math-Net.Ru

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     author = {E. E. D'yakonova},
     title = {Multitype {Galton{\textendash}Watson} branching processes in {Markovian} random environment},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2011_56_3_a7/}
}
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E. E. D'yakonova. Multitype Galton–Watson branching processes in Markovian random environment. Teoriâ veroâtnostej i ee primeneniâ, Tome 56 (2011) no. 3, pp. 592-601. http://geodesic.mathdoc.fr/item/TVP_2011_56_3_a7/

[1] Smith W. L., Wilkinson W., “On branching processes in random environments”, Ann. Math. Statist., 40:3 (1969), 814–827 | DOI | MR | Zbl

[2] Athreya K. B., Karlin S., “On branching processes with random environments. I: Extinction probabilities”, Ann. Math. Statist., 42:5 (1971), 1499–1520 | DOI | MR | Zbl

[3] Tanny D., “On multitype branching processes in a random environment”, Adv. Appl. Probab., 13:3 (1981), 464–497 | DOI | MR | Zbl

[4] Weissner E. W., “Multitype branching processes in random environments”, J. Appl. Probab., 8:1 (1971), 17–31 | DOI | MR | Zbl

[5] Kaplan N., “Some results about multidimensional branching processes with random environments”, Ann. Probab., 2:3 (1974), 441–455 | DOI | MR | Zbl

[6] Afanasev V. I., “Predelnaya teorema dlya kriticheskogo vetvyaschegosya protsessa v sluchainoi srede”, Diskret. matem., 5:1 (1993), 45–58 | MR

[7] Afanasyev V. I., Geiger J., Kersting G.,, Vatutin V. A., “Criticality for branching processes in random environment”, Ann. Probab., 33:2 (2005), 645–673 | DOI | MR | Zbl

[8] Geiger J., Kersting G., “The survival probability of a critical branching process in random environment”, Teoriya veroyatn. i ee primen., 45:3 (2000), 607–615 | MR | Zbl

[9] Vatutin V. A., Dyakonova E. E., “Vetvyaschiesya protsessy Galtona–Vatsona v sluchainoi srede. I: Predelnye teoremy”, Teoriya veroyatn. i ee primen., 48:2 (2003), 274–300 | Zbl

[10] Vatutin V. A., Dyakonova E. E., “Vetvyaschiesya protsessy Galtona–Vatsona v sluchainoi srede. II: Konechnomernye raspredeleniya”, Teoriya veroyatn. i ee primen., 49:2 (2004), 231–268 | Zbl

[11] Vatutin V. A., Dyakonova E. E., “Vetvyaschiesya protsessy v sluchainoi srede i butylochnye gorlyshki v evolyutsii populyatsii”, Teoriya veroyatn. i ee primen., 51:1 (2006), 22–46 | MR

[12] Vatutin V. A., Kyprianou A. E., “Branching processes in random environment die slowly”, Fifth Colloquium on Mathematics and Computer Science, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2008, 375–395 | MR

[13] Vatutin V. A., Vakhtel V. I., “Vnezapnoe vyrozhdenie kriticheskogo vetvyaschegosya protsessa v sluchainoi srede”, Teoriya veroyatn. i ee primen., 54:3 (2009), 417–438 | MR | Zbl

[14] Vatutin V. A., Dyakonova E. E., “Asimptoticheskie svoistva mnogotipnykh kriticheskikh vetvyaschikhsya protsessov, evolyutsioniruyuschikh v sluchainoi srede”, Diskret. matem., 22:2 (2010), 22–40

[15] Dyakonova E. E., “Ob asimptotike veroyatnosti nevyrozhdeniya mnogomernogo vetvyaschegosya protsessa v sluchainoi srede”, Diskret. matem., 11:1 (1999), 113–128 | Zbl

[16] Dyakonova E. E., “Kriticheskie mnogotipnye vetvyaschiesya protsessy v sluchainoi srede”, Diskret. matem., 19:4 (2007), 23–41

[17] Dyakonova E. E., Geiger J., Vatutin V. A., “On the survival probability and a functional limit theorem for branching processes in random environment”, Markov Process. Related Fields, 10:2 (2004), 289–306 | MR | Zbl

[18] D'Souza J. C., Hambly B. M., “On the survival probability of a branching process in a random environment”, Adv. Appl. Probab., 29:1 (1997), 38–55 | DOI | MR

[19] Kozlov M. V., “Ob asimptotike veroyatnosti nevyrozhdeniya kriticheskikh vetvyaschikhsya protsessov v sluchainoi srede”, Teoriya veroyatn. i ee primen., 21:4 (1976), 813–825 | MR | Zbl

[20] Kesten H., Spitzer F., “Convergence in distribution of products of random matrices”, Z. Wahrscheinlichkeitstheor. verw. Geb., 67:4 (1984), 363–386 | DOI | MR | Zbl

[21] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972, 414 pp.

[22] Athreya K. B., Ney P. E., Branching Processes, Springer, Berlin, 1972, 289 pp. | MR | Zbl

[23] Doney R. A., “Spitzer's condition and ladder variables in random walks”, Probab. Theory Related Fields, 101 (1995), 577–580 | DOI | MR | Zbl

[24] Sevastyanov B. A., Vetvyaschiesya protsessy, Nauka, M., 1971, 436 pp.

[25] Feller V., Vvedenie v teoriyu veroyatnoctei i ee prilozheniya, v. 2, Mir, M., 1984, 752 pp.