Naslov
On the power law tails in stationary branching models

Autori
Basrak, Bojan ; Kevei, Peter

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
Discussion Meeting on Stochastic Analysis, Geometry, and Random Fields

Mjesto i datum
Bangalore, Indija, 04.01.2020. - 10.01.2020

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
branching processes with immigration ; point processes ; limit theorems

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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