A scaling limit theorem for Galton-Watson processes in varying environments

Abstract

We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit theorem gives rise to the continuous-state branching processes in varying environments studied recently by several authors.

arXiv commentThis is a preliminary version of the paper published in Proc. Steklov Inst. Math. 316 (2022)

References in corpus (5)

• Criticality for branching processes in random environment
• Skew convolution semigroups and affine Markov processes
• Stochastic equations, flows and measure-valued processes
• Limit theorems for weakly subcritical branching processes in random environment
• Construction of continuous-state branching processes in varying environments