M. V. Kozlov
On large deviations of branching processes in a random environment: geometric distribution of descendants
A branching process Zn
with geometric distribution of descendants in a random environment represented by a sequence of independent identically distributed random variables (the Smith–Wilkinson model) is considered. The asymptotics of large deviation probabilities
P(ln Zn
> θn), θ > 0, are found provided that the steps of the accompanying random walk Sn
satisfy the Cramér condition. In the cases of supercritical, critical, moderate, and intermediate subcritical processes the asymptotics follow that of the large deviations probabilities
P(Sn
≤ θn). In strongly subcritical case the same asymptotics hold for θ greater than some θ* (for θ ≤ θ* the asymptotics of large deviation probabilities are different).
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 16, 03/2006
Pages: 155 - 174
Show full article (external site)
Show all available items of this journal
Search
