Voir la notice de l'article provenant de la source Math-Net.Ru
@article{TRSPY_2022_316_a9, author = {E. E. Dyakonova}, title = {Intermediately {Subcritical} {Branching} {Process} in a {Random} {Environment:} {The} {Initial} {Stage} of the {Evolution}}, journal = {Informatics and Automation}, pages = {129--144}, publisher = {mathdoc}, volume = {316}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a9/} }
TY - JOUR AU - E. E. Dyakonova TI - Intermediately Subcritical Branching Process in a Random Environment: The Initial Stage of the Evolution JO - Informatics and Automation PY - 2022 SP - 129 EP - 144 VL - 316 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a9/ LA - ru ID - TRSPY_2022_316_a9 ER -
E. E. Dyakonova. Intermediately Subcritical Branching Process in a Random Environment: The Initial Stage of the Evolution. Informatics and Automation, Branching Processes and Related Topics, Tome 316 (2022), pp. 129-144. http://geodesic.mathdoc.fr/item/TRSPY_2022_316_a9/
[1] Afanasyev V.I., Böinghoff Ch., Kersting G., Vatutin V.A., “Conditional limit theorems for intermediately subcritical branching processes in random environment”, Ann. Inst. Henri Poincaré. Probab. stat., 50:2 (2014), 602–627 | MR | Zbl
[2] 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
[3] Athreya K.B., Karlin S., “On branching processes with random environments. I: Extinction probabilities”, Ann. Math. Stat., 42:5 (1971), 1499–1520 | DOI | MR | Zbl
[4] Athreya K.B., Karlin S., “Branching processes with random environments. II: Limit theorems”, Ann. Math. Stat., 42:6 (1971), 1843–1858 | DOI | MR | Zbl
[5] Bertoin J., Lévy processes, Cambridge Tracts Math., 121, Cambridge Univ. Press, Cambridge, 1996 | MR
[6] Bertoin J., Doney R.A., “On conditioning a random walk to stay nonnegative”, Ann. Probab., 22:4 (1994), 2152–2167 | DOI | MR | Zbl
[7] Bingham N.H., Goldie C.M., Teugels J.L., Regular variation, Encycl. Math. Appl., 27, Cambridge Univ. Press, Cambridge, 1987 | MR | Zbl
[8] Chaumont L., “Excursion normalisée, méandre et pont pour les processus de Lévy stables”, Bull. sci. math., 121:5 (1997), 377–403 | MR | Zbl
[9] Chauvin B., Rouault A., Wakolbinger A., “Growing conditioned trees”, Stoch. Process. Appl., 39:1 (1991), 117–130 | DOI | MR | Zbl
[10] W. Feller, An Introduction to Probability Theory and Its Applications, v. 2, J. Wiley Sons, New York, 1971 | MR | MR | Zbl
[11] Kallenberg O., “Stability of critical cluster fields”, Math. Nachr., 77 (1977), 7–43 | DOI | MR | Zbl
[12] Kersting G., Vatutin V., Discrete time branching processes in random environment, J. Wiley Sons, Hoboken, NJ, 2017 | Zbl
[13] Lyons R., Pemantle R., Peres Y., “Conceptual proofs of $L\log L$ criteria for mean behavior of branching processes”, Ann. Probab., 23:3 (1995), 1125–1138 | DOI | MR | Zbl
[14] Neveu J., “Erasing a branching tree”, Adv. Apl. Probab., 18 (Suppl.) (1986), 101–108 | MR | Zbl
[15] Smith W.L., Wilkinson W.E., “On branching processes in random environments”, Ann. Math. Stat., 40 (1969), 814–827 | DOI | MR | Zbl
[16] Vatutin V., Dyakonova E., “Path to survival for the critical branching processes in a random environment”, J. Appl. Probab., 54:2 (2017), 588–602 | DOI | MR | Zbl
[17] V. A. Vatutin and E. E. Dyakonova, “The initial evolution stage of a weakly subcritical branching process in a random environment”, Theory Probab. Appl., 64:4 (2020), 535–552 | DOI | MR | Zbl