42 citations · 70 across the 8 of their papers we have counts for
6 papers · 2 filters
Limit Theorems for the Fractional Non-homogeneous Poisson Process
Nikolai Leonenko, Enrico Scalas, Mailan Trinh
The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse -stable subordinator. We propose a similar…
Correlated continuous time random walks and fractional Pearson diffusions
Nikolai N. Leonenko, Ivan Papić, Alla Sikorskii +1
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson dif…
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…
Heavy-tailed fractional Pearson diffusions
Nikolai N. Leonenko, Ivan Papić, Alla Sikorskii +1
We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are gov…
On rate of convergence in non-central limit theorems
Vo Anh, Nikolai Leonenko, Andriy Olenko +1
The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the…