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Path properties of Lévy driven mixed moving average processes
Danijel Grahovac, Péter Kevei, Orimar Sauri
We derive general sufficient conditions for the existence of càdlàg and continuous modifications of Lévy-driven mixed moving average processes. The conditions are explicit and easy…
Marcinkiewicz--Zygmund-type SLLN for mixed moving average processes
Danijel Grahovac, Péter Kevei, Dominik Mihalčić
The Marcinkiewicz--Zygmund theorem is a fundamental result in probability theory that establishes rates of convergence in the strong law of large numbers (SLLN). Although numerous…
Heavy-tailed critical Galton--Watson processes with immigration
Peter Kevei, Kata Kubatovics
Consider a critical Galton--Watson branching process with immigration, where the offspring distribution belongs to the domain of attraction of a -stable law with $α\in (0,…
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…
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…