Likely path to extinction in simple branching models with large initial population

[摘要] We give explicit formulae for most likely paths to extinction insimple branching models when initial population is large. Indiscrete time, we study theGalton-Watson process, and incontinuous time, the branching diffusion. The most likely pathsare found with the help of the large deviation principle (LDP). Wealso find asymptotics for the extinction probability, which gives a new expression in continuous time and recovers the known formula in discrete time. Due to thenonnegativity of the processes, the proof of LDP at the point ofextinction uses a nonstandard argument of independent interest.

[学科分类] 应用数学