TY - JOUR
T1 - Subcritical branching processes in a random environment without the Cramer condition
AU - Vatutin, Vladimir
AU - Zheng, Xinghua
PY - 2012/7
Y1 - 2012/7
N2 - A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of particles up to moment n given survival to this moment. Contrary to other types of subcritical BPRE, the limiting distribution is not discrete. We also show that the process survives for a long time owing to a single big jump of the associate random walk accompanied by a population explosion at the beginning of the process.
AB - A subcritical branching process in random environment (BPRE) is considered whose associated random walk does not satisfy the Cramer condition. The asymptotics for the survival probability of the process is investigated, and a Yaglom type conditional limit theorem is proved for the number of particles up to moment n given survival to this moment. Contrary to other types of subcritical BPRE, the limiting distribution is not discrete. We also show that the process survives for a long time owing to a single big jump of the associate random walk accompanied by a population explosion at the beginning of the process.
KW - Branching process
KW - Functional limit theorem
KW - Random environment
KW - Random walk
KW - Survival probability
UR - https://www.webofscience.com/wos/woscc/full-record/WOS:000305661000003
UR - https://openalex.org/W1984441917
UR - https://www.scopus.com/pages/publications/84861156411
U2 - 10.1016/j.spa.2012.04.008
DO - 10.1016/j.spa.2012.04.008
M3 - Journal Article
SN - 0304-4149
VL - 122
SP - 2594
EP - 2609
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 7
ER -