Abstract
We give explicit formulae for most likely paths to extinction in
simple branching models when initial population is large. In
discrete time, we study the Galton-Watson process, and in
continuous time, the branching diffusion. The most likely paths
are found with the help of the large deviation principle (LDP). We
also find asymptotics for the extinction probability,
which gives a new expression in continuous time and recovers
the known formula in discrete time. Due to the
nonnegativity of the processes, the proof of LDP at the point of
extinction uses a nonstandard argument of independent interest.