Likely path to extinction for simple branching model (Large Deviations approach)

Details Likely path to extinction for simple branching model (Large Deviations approach) Likely path to extinction for simple branching model (Large Deviations approach)

2005-07-13

arxiv.org/abs/math/0507257v5

Mathematics

Probability

Scientific paper

We give an explicit formula for the most likely path to extinction for the Galton-Watson processes with large initial population. We establish this result with the help of the large deviation principle (LDP) which also recovers the asymptotics of extinction probability. Due to the nonnegativity of the Galton-Watson processes, the proof of LDP verification at the point of extinction uses a nonstandard argument of independent interest.

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