Research

Research interest: Mainly, the link between nonlocal (partial) differential equations and stochastic processes, specifically subordinated and time-changed processes, and their applications in both deterministic and stochastic modelling, with particular attention to biological phenomena and population dynamics. In this branch, I also focus on stochastic simulation techniques for such kind of processes.

Together with this, I am also interested in Calculus of Variations (and variational methods for stochastic processes) and geometric theory of Banach function spaces.

Publications and Preprints:

  • F. Angrisani, G. Ascione, and G. Manzo, Atomic decomposition of finite signed measures on compacts of R^n, Annales Fennici Mathematici, accepted, 2021, arXiv: https://arxiv.org/abs/2004.13437

  • G. Ascione, A mass transportation proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem, submitted, 2021, arXiv: https://arxiv.org/abs/2105.08012

  • G. Ascione, Abstract Cauchy problems for the generalized fractional calculus, Nonlinear Analysis, 2021, doi: https://doi.org/10.1016/j.na.2021.112339

  • G. Ascione, D. Castorina, G. Catino, C. Mantegazza, A matrix Harnack inequality for semilinear heat equations, submitted, 2021, arXiv: https://arxiv.org/abs/2107.13846

  • G. Ascione, N. Leonenko, and E. Pirozzi, Time-non-local Pearson diffusions, Journal of Statistical Physiscs, 2021, doi: https://doi.org/10.1007/s10955-021-02786-2

  • G. Ascione, N. Leonenko, and E. Pirozzi, Non-local solvable birth-death processes, Journal of Theoretical Probability, 2021, doi: https://doi.org/10.1007/s10959-021-01087-4

  • G. Ascione, N. Leonenko, and E. Pirozzi, Fractional immigration-death processes, Journal of Mathematical Analysis and Applications, 2021, doi: https://doi.org/10.1016/j.jmaa.2020.124768

  • G. Ascione, N. Leonenko, and E. Pirozzi, On the transient behaviour of fractional M/M/1 queues, in Nonlocal and Fractional Operators, Springer, 2021, doi: https://doi.org/10.1007/978-3-030-69236-0_1

  • G. Ascione and J. Lőrinczi, Potentials for non-local Schrödinger operators with zero eigenvalues, submitted, 2021, arXiv: https://arxiv.org/abs/2005.13881

  • G. Ascione and J. Lőrinczi, Bulk behaviour of ground states for relativistic Schrödinger operators with compactly supported potentials, submitted, 2021, arXiv: https://arxiv.org/abs/2107.11580

  • G. Ascione, Y. Mishura, and E. Pirozzi, Fractional Ornstein-Uhlenbeck process with stochastic forcing, and its applications, Methodology and Computing in Applied Probability, 2021, doi: https://doi.org/10.1007/s11009-019-09748-y

  • G. Ascione, Y. Mishura, and E. Pirozzi, The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck process, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, accepted, 2021, arXiv: https://arxiv.org/abs/2005.12628

  • G. Ascione, Y. Mishura, and E. Pirozzi, Convergence results for the time-changed fractional Ornstein-Uhlenbeck processes, Theory of Probability and Mathematical Statistics, accepted, 2021, arXiv: https://arxiv.org/abs/2011.02733

  • G. Ascione and G. Paoli, The orthotropic p-Laplace eigenvalue problem of Steklov type as p->∞, Journal of Mathematical Analysis and Applications, 2021, doi: https://doi.org/10.1016/j.jmaa.2021.125219

  • M. Abundo, G. Ascione, M. F. Carfora, and E. Pirozzi, A fractional PDE for first passage time of time-changed Brownian motion and its numerical solution, Applied Numerical Mathematics, 2020, doi: https://doi.org/10.1016/j.apnum.2019.07.020

  • F. Angrisani, G. Ascione, L. D'Onofrio, and G. Manzo, Duality and distance formulas in Lipschitz-Hölder spaces, Rendiconti Lincei- Matematica e Applicazioni, 2020, doi: https://doi.org/10.4171/RLM/897.

  • G. Ascione, On the construction of some deterministic and stochastic non-local SIR models, Mathematics, 2020, doi: https://doi.org/10.3390/math8122103

  • G. Ascione, Simulation of an α-stable time-changed SIR model, in International Conference on Computer Aided Systems Theory, Springer, 2020, doi: https://doi.org/10.1007/978-3-030-45093-9_27

  • G. Ascione, G. D'Onofrio, L. Kostal, and E. Pirozzi, An optimal Gauss-Markov approximation for a process with stochastic drift and applications, Stochastic Processes and their Applications, 2020, doi: https://doi.org/10.1016/j.spa.2020.05.018

  • G. Ascione, N. Leonenko, and E. Pirozzi, Fractional Erlang queues, Stochastic Processes and their Applications, 2020, doi: https://doi.org/10.1016/j.spa.2019.09.012

  • G. Ascione and G. Manzo, o-O structure of some rearrangement invariant Banach function spaces, Journal of Elliptic and Parabolic Equations, 2020, doi: https://doi.org/10.1007/s41808-020-00051-3

  • G. Ascione, Y. Mishura, and E. Pirozzi, Time-changed fractional Ornstein-Uhlenbeck process, Fractional Calculus and Applied Analysis, 2020, doi: https://doi.org/10.1515/fca-2020-0022

  • G. Ascione and E. Pirozzi, On the construction of some fractional stochastic Gompertz models, Mathematics, 2020, doi: https://doi.org/10.3390/math8010060

  • G. Ascione, E. Pirozzi, and B. Toaldo, On the exit time from open sets of some semi-Markov processes, Annals of Applied Probability, 2020, doi: https://doi.org/10.1214/19-AAP1525

  • F. Angrisani, G. Ascione, and G. Manzo, Orlicz spaces with a o-O type structure, Ricerche di Matematica, 2019, doi: https://doi.org/10.1007/s11587-019-00441-3

  • G. Ascione, M. F. Carfora, and E. Pirozzi, A stochastic model for interacting neurons in the olfactory bulb, Biosystems, 2019, doi: https://doi.org/10.1016/j.biosystems.2019.104030

  • G. Ascione and E. Pirozzi, On a stochastic neuronal model integrating correlated inputs, Mathematical Biosciences and Engeneering, 2019, doi: https://doi.org/10.3934/mbe.2019260

  • G. Ascione and B. Toaldo, A Semi-Markov Leaky Integrate-and-Fire Model, Mathematics, 2019, doi: https://doi.org/10.3390/math7111022

  • F. Angrisani and G. Ascione, A note on VLO functions, Rendiconto dell'Accademia delle Scienze Fisiche e Matematiche, 2018.

  • G. Ascione, N. Leonenko, and E. Pirozzi, Fractional queues with catastrophes and their transient behaviour, Mathematics, 2018, doi: https://doi.org/10.3390/math6090159

  • F. Angrisani, G. Ascione, C. Leone, and C. Mantegazza, Appunti di Calcolo delle Variazioni, Amazon, 2019.

  • G. Ascione and E. Pirozzi, On fractional stochastic modeling of neuronal activity including memory effects, in International Conference on Computer Aided Systems Theory, Springer, 2018, doi: https://doi.org/10.1007/978-3-319-74727-9_1