2 citations · 5 across the 8 of their papers we have counts for
9 papers
Beta-weighted non-local differential operators and related stochastic processes
L. Beghin, N. Leonenko, T. Simon +1
In this work we introduce a class of non-local differential operators defined through a beta-weighted averaging of the ordinary derivative. We investigate their analytical properti…
Multiscaling asymptotic behavior of solutions to random high-order heat equations
Maha Mosaad A Alghamdi, Nikolai Leonenko, Andriy Olenko
This paper studies high-order partial differential equations with random initial conditions that have both long-memory and cyclic behavior. The cases of random initial conditions w…
Tossing half-coins and other partial coins: signed probabilities and Sibuya distribution
Nikolai Leonenko, Igor Podlubny
A method for the numerical simulation of signed probability distributions for the case of tossing -th of a coin is presented and illustrated by examples.
Construction and limit theorems for supCAR fields
Illia Donhauzer, Nikolai Leonenko, Andriy Olenko
The paper introduces a new class of random fields, supCAR fields, which are constructed as superpositions of continuous autoregressive random fields. These supCAR fields possess in…
Stretched non-local Pearson diffusions
Luisa Beghin, Nikolai Leonenko, Ivan Papić +1
We define a novel class of time changed Pearson diffusions, termed stretched non local Pearson diffusions, where the stochastic time change model has the Kilbas Saigo function as i…
Sibuya probability distributions and numerical evaluation of fractional-order operators
Nikolai Leonenko, Igor Podlubny
In this work we explore the Sibuya discrete probability distribution, which serves as the basis and the main instrument for numerical simulations of Grunwald--Letnikov fractional d…
Relaxation equations with stretched non-local operators: renewal and time-changed processes
Luisa Beghin, Nikolai Leonenko, Jayme Vaz
We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through ``stretched" non-local operators (of order and with paramete…
Multiscaling limit theorems for stochastic FPDE with cyclic long-range dependence
Maha Mosaad A Alghamdi, Nikolai Leonenko, Andriy Olenko
The paper studies solutions of stochastic partial differential equations with random initial conditions. First, it overviews some of the known results on scaled solutions of such e…
On Fractional Spherically Restricted Hyperbolic Diffusion Random Field
Nikolai Leonenko, Andriy Olenko, Jayme Vaz
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are give…