engleski

On the power law tails in stationary branching models

Using the example of stationary subcritical branching processes with immigration, we discuss how power law tails arise in two entirely different ways. It is not entirely surprising that the regular variation of the immigrant distribution induces the same property for the stationary distribution, see e.g. [1]. In this talk, we explain how the assumption that the branching takes place in a random environment again generates power law tail behavior of the stationary distribution. We analyze probabilistic properties of the resulting stationary process in both cases. The original motivation comes from Kesten, Kozlov, and Spitzer seminal paper [2], which relates a random walk in random environment model to a special Galton–Watson process with immigration in random environment.

branching processes with immigration ; point processes ; limit theorems

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