1. School of Mathematical Sciences, Monash University , Victoria, Australia fima.klebaner@sci.monash.edu.au;3. Electrical Engineering-Systems, Tel Aviv University , Tel Aviv, Israel
Abstract:
Cramer's classical theorem is applied to obtain large deviations in branching processes. This is a new avenue for analysis of models in discrete and continuous time. For the Galton-Watson process a new formula for the rate function in terms of the Legendre transform of its offspring distribution is derived. Further analysis of the approximate path to extinction produces a new interesting formula.