2009/03/10 by López-Mimbela, José Alfredo, Salas, Antonio Murillo
#60F15 #60J80 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.0903.1871
The occupation time of an age-dependent branching particle system in \Rd is considered, where the initial population is a Poisson random field and the particles are subject to symmetric α-stable migration, critical binary branching and random lifetimes. Two regimes of lifetime distributions are considered: lifetimes with finite mean and lifetimes belonging to the normal domain of attraction of a γ-stable law, γ∈(0,1). It is shown that in dimensions d>αγ for the heavy-tailed lifetimes case, and d>α for finite mean lifetimes, the occupation time proccess satisfies a strong law of large numbers.