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pro vyhledávání: '"Grahovac, Danijel"'
Autor:
Grahovac, Danijel, Kevei, Peter
In this paper we consider sample path growth of superpositions of positive Ornstein--Uhlenbeck type processes (supOU). SupOU are stationary infinitely divisible processes defined as integrals with respect to a random measure. They allow marginal dist
Externí odkaz:
http://arxiv.org/abs/2402.08584
Autor:
Grahovac, Danijel, Kevei, Peter
Superpositions of Ornstein-Uhlenbeck processes allow a flexible dependence structure, including long range dependence for OU-type processes. Their complex asymptotic is governed by three effects: the behavior of the L\'evy measure both at infinity an
Externí odkaz:
http://arxiv.org/abs/2402.01196
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 provide a deeper understanding of these intricate limiting phenomena.
Externí odkaz:
http://arxiv.org/abs/2104.06006
Autor:
Grahovac, Danijel
Publikováno v:
Chaos, Solitons & Fractals, (2020) 134(109735)
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 beyond the original cascade construction of Mandelbrot. We provide a ne
Externí odkaz:
http://arxiv.org/abs/2003.09159
Autor:
Grahovac, Danijel
Publikováno v:
Statistics & Probability Letters. 187 (2022) 109507
In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds typically only u
Externí odkaz:
http://arxiv.org/abs/1912.03977
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU processes h
Externí odkaz:
http://arxiv.org/abs/1904.00100
The so-called "supOU" processes, namely the superpositions of Ornstein-Uhlenbeck type processes are stationary processes for which one can specify separately the marginal distribution and the dependence structure. They can have finite or infinite var
Externí odkaz:
http://arxiv.org/abs/1806.09811
Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently. We show that they can also display inte
Externí odkaz:
http://arxiv.org/abs/1711.09623
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 define separately the marginal distribution and the dependence struct
Externí odkaz:
http://arxiv.org/abs/1708.02762
Superpositions of Ornstein-Uhlenbeck type (supOU) processes form a rich class of stationary processes with a flexible dependence structure. The asymptotic behavior of the integrated and partial sum supOU processes can be, however, unusual. Their cumu
Externí odkaz:
http://arxiv.org/abs/1708.02178