On the asymptotic behavior of a dynamic version of the neyman contagious point process

Abstract

We consider a dynamic version of the Neyman contagious point process that can be used for modeling the spacial dynamics of biological populations, including species invasion scenarios. Starting with an arbitrary finite initial configuration of points in with nonnegative weights, at each time step a point is chosen at random from the process according to the distribution with probabilities proportional to the points weights. Then a finite random number of new points is added to the process, each displaced from the location of the chosen "mother" point by a random vector and assigned a random weight. Under broad conditions on the sequences of the numbers of newly added points, their weights an..