Large Deviation Rates for Controlled Branching Processes

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

Large Deviation (LD) theory is crucial for deriving statistical results in stochastic modeling. In the standard Bienaymé-Galton-Watson Process (BGWP), LD analysis of the offspring mean estimator—the ratio between consecutive generation sizes—is vital for calculating amplification rates in quantitative PCR experiments.

This work extends these results to Controlled Branching Processes (CBP). A CBP generalizes the BGWP by introducing a random control function that determines the number of progenitors in each generation. Our objective is to establish new LD results for CBPs under two scenarios: Analysis based on the existence of exponential or polynomial moments and results derived from the asymptotic properties of the harmonic moments of generation sizes.

Keywords: Controlled Branching Processes,Large Deviations,exponential moments, polynomial momento, Harmonic Moments

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

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