Завершено12 сентября 2013 года

On the asymptotic behaviour of a dynamic version of the Neyman contagious point process

1696-е заседание (номер восстановлен по хронологии).

Konstantin Borovkov (University of Melbourne)
On the asymptotic behaviour of a dynamic version of the Neyman contagious point process
We consider a dynamic version of the Neyman contagious point process that can be used for modelling the spacial dynamics of a biological population, including species invasion scenarios. Starting with an arbitrary finite initial configuration of points in Rd 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 random number of new points is added to the process, each displaced from the location of the chosen point by a random vector and assigned a random weight. Under broad conditions on the sequences of the numbers of newly added points (which include a random environments setup), their weights and displacement vectors, we derive the asymptotic behaviour of the point added to the process at time step n and also that of the scaled mean measure of the point process after time step n→∞. See arXiv:1308.5783