Large deviations for Branching Processes in Random Environment
By Vincent Bansaye, J. Berestycki. 2008
62 citations recorded by the source corpus.
A branching process in random environment (Zn, n ∈ N) is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of large deviations. By contrast to the Galton-Watson case, here random environments and the branching process can conspire to achieve atypical events such as Zn ≤ e cn when c is smaller than the typical geometric growth rate ¯ L and Zn ≥ e cn when c > ¯ L. One way to obtain such an atypical rate of growth is to have a typical realization of the branching process in an atypical sequence of environments. This gives us a general lower bound for the rate of decrease of their probability. When each individual leaves at least one offspring in the next generation almost surely, we compute the exact rate function of these events and we show that condi
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/54d6a953a6effb720d2fecfbec6d1a9098ad09d3
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Citations in the corpus
- Moments, moderate and large deviations for a branching process in a random environment (2010, methodology): “The study of asymptotic properties of a branching process in a random environment has recently received attention, see for example Afanasyave, Geiger, Kersting & Vatutin (2005, [1] & [2]), Kozlov (2006, [16]), Bansaye & Berestycki (2009, [5]), Bansaye & Böinghoff (2010, [6]), Böinghoff & Kersting (2”