Abstract:
For an extended class of multitype critical branching processes in a random environment, the asymptotic behaviour of the survival probability is found under the conditions which are weaker than those known earlier even for the single-type case. A functional limit theorem is proved for the number of particles in the process at moments nt, 0≤t≤1, conditioned on its survival up to moment n.
Citation:
V. A. Vatutin, E. E. Dyakonova, “Asymptotic properties of multitype critical branching processes evolving in a random environment”, Diskr. Mat., 22:2 (2010), 22–40; Discrete Math. Appl., 20:2 (2010), 157–177
This publication is cited in the following 12 articles:
V. A. Vatutin, E. E. Dyakonova, “Multitype branching processes in random environment”, Russian Math. Surveys, 76:6 (2021), 1019–1063
V. A. Vatutin, E. E. D'yakonova, “The Survival Probability for a Class of Multitype Subcritical Branching Processes in Random Environment”, Math. Notes, 107:2 (2020), 189–200
V. A. Vatutin, E. E. Dyakonova, “Branching processes in random environment with sibling dependence”, J. Math. Sci. (N.Y.), 246:4 (2020), 569–579
V. A. Vatutin, E. E. D'yakonova, “Multitype weakly subcritical branching processes in random environment”, Discrete Math. Appl., 31:3 (2021), 207–222
V. A. Vatutin, E. E. D'yakonova, “Multitype branching processes in random environment: survival probability for the critical case”, Theory Probab. Appl., 62:4 (2018), 506–521
Discrete Time Branching Processes in Random Environment, 2017, 275
Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Discrete Math. Appl., 28:1 (2018), 7–22
E. E. D'yakonova, “Limit theorem for multitype critical branching process evolving in random environment”, Discrete Math. Appl., 25:3 (2015), 137–147
V. A. Vatutin, E. E. Dyakonova, S. Sagitov, “Evolution of branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 220–242
E. E. Dyakonova, “Multitype subcritical branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 80–89
E. E. D'yakonova, “Multitype branching processes evolving in a Markovian environment”, Discrete Math. Appl., 22:5-6 (2012), 639–664
E. E. D'yakonova, “Multitype Galton–Watson branching processes in Markovian random environment”, Theory Probab. Appl., 56:3 (2011), 508–517
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