25 citations · 87 across the 17 of their papers we have counts for
19 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 càdlàg and continuous modifications of Lévy-driven mixed moving average processes. The conditions are explicit and easy…
Superpositions of CARMA processes
Danijel Grahovac, Magdalena Mikić
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-Uhl…
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…
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…
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…
Intermittency and multiscaling in limit theorems
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we…
Multifractal processes: Definition, properties and new examples
Danijel Grahovac
We investigate stochastic processes possessing scale invariance properties which we refer to as multifractal processes. The examples of such processes known so far do not go much b…
Intermittency in the small-time behavior of Lévy processes
Danijel Grahovac
In this paper we consider convergence of moments in the small-time limit theorems for Lévy processes. We provide precise asymptotics for all the absolute moments of positive order.…
Intermittency and infinite variance: the case of integrated supOU processes
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence…
The multifaceted behavior of integrated supOU processes: The infinite variance case
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribut…
Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure…
Intermittency of trawl processes
Danijel Grahovac, Nikolai N. Leonenko, Murad S. Taqqu
We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to…
The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes
Danijel Grahovac, Nikolai N. Leonenko, Anna Sikorskii +1
Superpositions of Ornstein-Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrate…
The scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends
Florin Avram, Danijel Grahovac, Ceren Vardar-Acar
First passage problems for spectrally negative Lévy processes with possible absorbtion or/and reflection at boundaries have been widely applied in mathematical finance, risk, queue…
Intermittency of Superpositions of Ornstein-Uhlenbeck Type Processes
Danijel Grahovac, Nikolai N. Leonenko, Alla Sikorskii +1
The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on Lévy driven Ornstein-Uhlenbeck (OU) type proc…
Bounds on the support of the multifractal spectrum of stochastic processes
Danijel Grahovac, Nikolai N. Leonenko
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the s…
Asymptotic Properties of the Partition Function and Applications in Tail Index Inference of Heavy-Tailed Data
Danijel Grahovac, Mofei Jia, Nikolai N. Leonenko +1
The so-called partition function is a sample moment statistic based on blocks of data and it is often used in the context of multifractal processes. It will be shown that its behav…