Geodesic
On large deviations of a branching process in random environments with immigration at moments of extinction
Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 36-42

Voir la notice de l'article provenant de la source Math-Net.Ru

Let ($Z_{n}^{*}$) be a branching process in independent identically distributed random environments with (conditioned on the environments) geometric distribution of the number of offsprings and immigration of independent identically distributed numbers of new particles at moments of extinction. Supposing that the increments of the accompanying random walk ($S_n$) and numbers of immigrants satisfy right-hand Cramér condition we obtain the asymptotics of large deviation probabilities $P(\text{ln}\, Z_{n}^{*}\geqslant\theta n)$.
Keywords: large deviations, Cramér condition, branching processes, random environments, processes with immigration. 
@article{DM_2014_26_4_a3,
     author = {D. V. Dmitrushchenkov},
     title = {On large deviations of a branching process in random environments with immigration at moments of extinction},
     journal = {Diskretnaya Matematika},
     pages = {36--42},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2014_26_4_a3/}
}
TY  - JOUR
AU  - D. V. Dmitrushchenkov
TI  - On large deviations of a branching process in random environments with immigration at moments of extinction
JO  - Diskretnaya Matematika
PY  - 2014
SP  - 36
EP  - 42
VL  - 26
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2014_26_4_a3/
LA  - ru
ID  - DM_2014_26_4_a3
ER  - 
%0 Journal Article
%A D. V. Dmitrushchenkov
%T On large deviations of a branching process in random environments with immigration at moments of extinction
%J Diskretnaya Matematika
%D 2014
%P 36-42
%V 26
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2014_26_4_a3/
%G ru
%F DM_2014_26_4_a3
D. V. Dmitrushchenkov. On large deviations of a branching process in random environments with immigration at moments of extinction. Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 36-42. http://geodesic.mathdoc.fr/item/DM_2014_26_4_a3/