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math.PR2024
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…
math.PR2024
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…
math.PR2024
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…