Likely path to extinction for simple branching model (Large Deviations approach)
F. Klebaner, R. Liptser
Abstract
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.
Create a lesson
Related papers
Mean convergence for Banach space-valued random elements indexed in measure spaces
Nguyen Thi Kim Sang, Nguyen Tran Thuan
Extinction and extinguishment properties for a nonlinear predator-prey branching model
Lina Ji, Jie Xiong, Wen Xu et al.
Multihomogeneous Measures and Stochastic Polar Representations
Enkelejd Hashorva
Cramér transform, half-space depth and threshold phenomena for convex bodies
Minas Pafis
Equilibrium fluctuations of the weakly asymmetric inclusion process
Simon Gabriel
Counterexamples to the site-percolation analogues of the Easo-Severo-Tassion cutset theorems
Joel Bassil