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Functional limit theorem for branching processes in nearly degenerate varying environment
Peter Kevei, Kata Kubatovics
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out…
Generalized Rényi statistics
Péter Kevei, László Viharos
In Rényi's representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic generalized Rényi…
Tail behavior and almost sure growth rate of supOU processes
Danijel Grahovac, Peter Kevei
In this paper we consider sample path growth of superpositions of Ornstein--Uhlenbeck type processes (supOU). SupOU processes are stationary infinitely divisible processes defined…
Almost sure growth of integrated supOU processes
Danijel Grahovac, Peter Kevei
Superpositions of Ornstein-Uhlenbeck processes allow a flexible dependence structure, including long range dependence for OU-type processes. Their complex asymptotics are governed…
Branching Processes with Immigration in a Random Environment -- the Grincevičius--Grey setup
Peter Kevei
We determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the of…