English

Rates on Yaglom's limit for Galton-Watson processes in a varying environment

Probability 2024-10-03 v2

Abstract

A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable normalization of the process conditioned on non-extinction converges in distribution to a standard exponential random variable. In this manuscript, we provide the rate of convergence of the Yaglom limit with respect to the Wasserstein metric.

Keywords

Cite

@article{arxiv.2305.11801,
  title  = {Rates on Yaglom's limit for Galton-Watson processes in a varying environment},
  author = {Natalia Cardona-Tobón and Arturo Jaramillo and Sandra Palau},
  journal= {arXiv preprint arXiv:2305.11801},
  year   = {2024}
}

Comments

22 pages. Corrected some minor errors in the introduction, specifically in Theorem 1.2 and Equation 1.3. Added new references