Extinction Time Tail Behavior and existence of Yaglom Limits in Subcritical Controlled Branching Processes

C. Cañada Moreno, M. González Velasco, I. M. del Puerto García

We investigate the asymptotic behavior of subcritical controlled branching processes (CBPs) with random control with zero an absorbing state. We determine the asymptotic decay rate of the survival probability. By using the spectral theory of positive linear operators, we prove that under suitable moment conditions, the transition operator is quasi-compact. This framework allows us to formally link the geometric decay of the survival probability to the tail behavior of the time to extinction, and further provides a precise asymptotic characterization of the expected extinction time through the dominant spectral elements. We also establish the existence of a Yaglom limit (quasi-stationary distribution) for the process conditioned on non-extinction.

Keywords: Markov Chain, Controlled Branching Process, Extinction time, Yaglom limit, Quasi-estacionary distribution, Spectral Radius.

GT Procesos Estocásticos y sus Aplicaciones III
September 3, 2026  9:00 AM
Aula 26

I. M. del Puerto García, M. González Velasco, C. Minuesa Abril, A. N. Vidyashankar

I. Garin, J. Doncel

M. González, R. E. Lillo, P. Ramírez-Cobo, L. Senade