Abstract:
We investigate a multitype critical branching process in an i.i.d. random environment. A functional limit theorem is proved for the logarithm of the number of particles in the process at moments nt,0≤t≤1,conditioned on its survival up to moment n→∞.
Keywords:
multitype branching processes, random environment, functional limit theorem.
Citation:
E. E. D'yakonova, “Limit theorem for multitype critical branching process evolving in random environment”, Diskr. Mat., 27:1 (2015), 44–58; Discrete Math. Appl., 25:3 (2015), 137–147
This publication is cited in the following 7 articles:
Ion Grama, Quansheng Liu, Erwan Pin, “A Kesten–Stigum type theorem for a supercritical multitype branching process in a random environment”, Ann. Appl. Probab., 33:2 (2023)
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. D'yakonova, “Properties of multitype subcritical branching processes in random environment”, Discrete Math. Appl., 31:5 (2021), 367–382
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 branching processes in random environment: survival probability for the critical case”, Theory Probab. Appl., 62:4 (2018), 506–521
Elena E. D'yakonova, “Reduced multitype critical branching processes in random environment”, Discrete Math. Appl., 28:1 (2018), 7–22
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