6 papers · 1 filter
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.
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 paramet…
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…
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…
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 PapiÄ +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…