5 papers
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…