engleski

On subcritical branching processes with regularly varying immigration

Provided that a stationary multivariate regularly varying time series satisfies certain weak dependence conditions, its extremal behavior can be elegantly characterized using the theory of point processes and the notion of the tail process. However, except in a few simple cases, establishing such conditions and determining exact distribution of the tail process in the multivariate setting remains a technically challenging task. We discuss a class of models where one can follow a somewhat different route to asymptotic analysis. The presentation is motivated by the study of conditional least squares estimator of the mean number of progeny in the branching process with heavy tailed immigration. We also exhibit the rate of convergence and precise asymptotic distribution of the estimator.

branching processes with immigration ; point processes ; limit theorems

nije evidentirano