Large deviation results in controlled branching processes

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

The topic of large deviation (LD) plays an important role on many results in statistics. Among others results, the LD behavior of the statistic that determines rate between the populations of two consecutive generations has been studied. This statistic has been used in the estimation of the amplification rate in a quantitative polymerase chain reaction (PCR) experiment where only the population sizes of such a generations are observed. In this talk we will focus on LD results in the framework of controlled branching processes (CBP). These are a generalization of standard Galton-Watson processes where at each generation the number of progenitors is randomly chosen through a random control function. The aim of this work is to develop LD results for CBPs under an assumption on the exponential moments or polynomial moments of the offspring distribution and also based on the asymptotic behaviour of the harmonic moments of the generation sizes.

Keywords: Large deviation, branching processes, controlled branching processes

GT15.PROCEST2 Invited Session
November 10, 2023  9:30 AM
CC3: Room 1

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A. De la Peña Cuao, A. Barrera Garcia, F. A. Torres Ruiz

F. J. Villarroel Rodriguez, F. J. Villarroel Rodriguez

J. E. Ruiz Castro, H. Zapata Ceballos