Langevin equation in complex media and anomalous diffusion

S Vitali, V Sposini, O Sliusarenko… - Journal of The …, 2018 - royalsocietypublishing.org
The problem of biological motion is a very intriguing and topical issue. Many efforts are
being focused on the development of novel modelling approaches for the description of …

The Fokker–Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm

C Runfola, S Vitali, G Pagnini - Royal Society Open …, 2022 - royalsocietypublishing.org
By collecting from literature data experimental evidence of anomalous diffusion of passive
tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live …

[HTML][HTML] Mittag-Leffler analysis II: Application to the fractional heat equation

M Grothaus, F Jahnert - Journal of Functional Analysis, 2016 - Elsevier
Mittag-Leffler analysis is an infinite dimensional analysis with respect to non-Gaussian
measures of Mittag-Leffler type which generalizes the powerful theory of Gaussian analysis …

[HTML][HTML] On semi-Markov processes and their Kolmogorov's integro-differential equations

E Orsingher, C Ricciuti, B Toaldo - Journal of Functional Analysis, 2018 - Elsevier
Semi-Markov processes are a generalization of Markov processes since the exponential
distribution of time intervals is replaced with an arbitrary distribution. This paper provides an …

Centre-of-mass like superposition of Ornstein–Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

M D'Ovidio, S Vitali, V Sposini… - … Calculus and Applied …, 2018 - degruyter.com
We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of
relaxation times and a population of noise amplitudes that characterize the heterogeneity of …

Semi-Markov processes, integro-differential equations and anomalous diffusion-aggregation

M Savov, B Toaldo - Annales de l'Institut Henri Poincaré …, 2020 - projecteuclid.org
Dans cet article, les équations de Volterra intégro-différentielles dont le noyau de
convolution dépend de la variable vectorielle sont considérées et une relation entre ces …

Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method

Ł Płociniczak, M Świtała - Fractional Calculus and Applied Analysis, 2022 - Springer
The aim of this work is to devise and analyse an accurate numerical scheme to solve Erdélyi–
Kober fractional diffusion equation. This solution can be thought as the marginal pdf of the …

Generalized Fokker–Planck equation for superstatistical systems

C Runfola, G Pagnini - Physica D: Nonlinear Phenomena, 2024 - Elsevier
Superstatistical systems are non-equilibrium systems in stationary states with large
fluctuations of intensive quantities. Different effective statistical processes follow accordingly …

Integral representation of generalized grey Brownian motion

W Bock, S Desmettre, JL da Silva - Stochastics, 2020 - Taylor & Francis
In this paper, we investigate the representation of a class of non-Gaussian processes,
namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic …

A class of infinite-dimensional Gaussian processes defined through generalized fractional operators

L Beghin, L Cristofaro, Y Mishura - arXiv preprint arXiv:2309.13283, 2023 - arxiv.org
The generalization of fractional Brownian motion in infinite-dimensional white and grey
noise spaces has been recently carried over, following the Mandelbrot-Van Ness …