Occupation time fluctuations of an age-dependent critical binary branching particle system

2023/01/27 by López-Mimbela, José Alfredo, Murillo-Salas, Antonio, Ramírez-González, José Hermenegildo · 1 citation
#60E10 #60J80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2301.11540

Abstract

We study the limit fluctuations of the rescaled occupation time process of a branching particle system in ℝ^d, where the particles are subject to symmetric α-stable migration (0<α≤2), critical binary branching, and general non-lattice lifetime distribution. We focus on two different regimes: lifetime distributions having finite expectation, and Pareto-type lifetime distributions, i.e. distributions belonging to the normal domain of attraction of a γ-stable law with γ∈(0,1). In the latter case we show that, for dimensions αγ

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