7 papers · 1 filter
Path properties of Lévy driven mixed moving average processes
Danijel Grahovac, Péter Kevei, Orimar Sauri
We derive general sufficient conditions for the existence of cà dlà g and continuous modifications of Lévy-driven mixed moving average processes. The conditions are explicit and e…
Superpositions of CARMA processes
Danijel Grahovac, Magdalena MikiÄ
We introduce supCARMA processes, defined as superpositions of Lévy-driven CARMA processes with respect to a Lévy basis, as a natural extension of the superpositions of Ornstein-U…
Marcinkiewicz--Zygmund-type SLLN for mixed moving average processes
Danijel Grahovac, Péter Kevei, Dominik MihalÄiÄ
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…
Integer-valued multifractal processes
Danijel Grahovac
Multifractal scaling has been extensively studied for real-valued stochastic processes, but a systematic integer-valued analogue has remained largely unexplored. In this work, we i…
Dickman type stochastic processes with short- and long- range dependence
Danijel Grahovac, Anastasiia Kovtun, Nikolai N. Leonenko +1
We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a…
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…