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Title: Large deviation results for controlled branching processes with immigration Authors:  Miguel Gonzalez Velasco - University of Extremadura (Spain)
Carmen Minuesa Abril - University of Extremadura (Spain)
Ines M del Puerto - University of Extremadura (Spain) [presenting]
Anand Vidyashankar - George Mason University (United States)
Abstract: A control branching process (CBP) is a generalization of Byenaime-Galton-Watson processes where at each generation, the number of progenitors is randomly chosen through a random control function. We modify a CBP, including the possibility of immigration of individuals at each generation. The aim is to give several large deviation results for the CBP with immigration. We consider the supercritical case and establish the rate of convergence of the process normalized by the number of progenitors to the offspring mean and of the ratio of successive generations to the growth rate of the process. We analyze the large deviations under an assumption on the exponential moments of the offspring and immigration distributions and also based on the asymptotic behaviour of the harmonic moments of the generation and control sizes.