Giacomo Ascione
Ricercatore in tenure track
- GSD 01/MATH-03 ; SSD MATH-03/B
- g.ascione@ssmeridionale.it
- Via Mezzocannone, n.4-80134 (NA)
- Area Interdisciplinare Scientifico-Tecnologica
Bio
I got my Bachelor in Mathematics in 2015 at Università degli Studi di Napoli Federico II, with a thesis (in Analysis) titled “Misure di Haudorff”, under the supervision of Prof. Nicola Fusco.
I took my Master degree in Mathematics in 2017, still at Università degli Studi di Napoli Federico II, with a thesis (in Probability) titled “On fractional Ornstein-Uhlenbeck processes”, under the supervition of Prof. Enrica Pirozzi.
I got my PhD at Università degli Studi di Napoli Federico II. More precisely, I defended my PhD thesis, titled “Probabilistic approach to non-local equations”, in March 2021.
Starting from November 2021, I had been a Postdoc in Scuola Superiore Meridionale for 3 years.
Right now, I am a Researcher (RTT) at Scuola Superiore Meridionale .
Ricerca
My research topics focus on the relation between stochastic processes and (mostly linear) integro-differential equations. Precisely, my main interest concerns non-local operators and equations involving them either in the space or in the time variable. In the first context, I studied in particular relativistic (or more generally nonlocal) Schrödinger operators, with particular attention to their spectrum. In the latter, I worked on the connection between semi-Markov processes and time-nonlocal/delayed equations, where the delay is applied to the time derivative term.
Lately, I’m also studying mean field sparse optimal control problems related to leader-follower systems, by making use of tools coming from the theory of stochastic differential equations.
Other research topics I currently work on concern isoperimetric problems related to nonlocal operators and deterministic control and approximation of stochastic differential equations.
Pubblicazioni
Some Publications:
-Anceschi, A., Castorina, Solombrino: Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift, Journal of Mathematical Analysis and Applications, 2025
–A., Vidotto: Time-changed spherical Brownian motions with longitudinal drifts, Stochastic Processes and their Applications, 2025
–A., Savov, Toaldo: Regularity and asymptotics of densities of inverse subordinators, Transactions of the London Mathematical Society, 2024
–A., Lőrinczi: Bulk behaviour of ground states for relativistic Schrödinger operators with compactly supported potentials, Annales Henri Poincare, 2024
–A., Castorina, Solombrino: Mean field sparse optimal control of systems with additive white noise, SIAM Journal of Mathematical Analysis, 2023
–A., D’Onofrio: Deterministic control of SDEs with stochastic drift and multiplicative noise: a variational approach, Journal of Applied Mathematics & Optimization, 2023
–A., Cuomo: A sojourn based approach to semi-Markov reinforcement learning, Journal of Scientific Computing, 2022
–A., Mishura, Pirozzi: The Fokker-Planck equation for the time-changed fractional Ornstein-Uhlenbeck stochastic process, Proceedings of the Royal Society of Edinburgh, 2022
–A., Lőrinczi: Potentials for non-local Schrödinger operators with zero eigenvalues, Journal of Differential Equations, 2022
–A.: A spherical rearrangement proof of the stability of a Riesz-type inequality and an application to an isoperimetric type problem, ESAIM: Control, Optimisation and Calculus of Variations, 2022
–A., Paoli: The orthotropic p-Laplace eigenvalue problem of Steklov type as p→+∞, Journal of Mathematical Analysis and Applications, 2021
–A.: Abstract Cauchy Problems for the generalized fractional calculus, Nonlinear Analysis, 2021
–A., Leonenko, Pirozzi: Time-non-local Pearson diffusions, Journal of Statistica Physics, 2021
–A., Manzo: o-O structure of some rearrangement invariant Banach function spaces, Journal of Elliptic and Parabolic Equations, 2020
–A., Leonenko, Pirozzi: Fractional Erlang Queues, Stochastic Processes and their Applications, 2020
-Angrisani, A., D’Onofrio, Manzo: Duality and distance formulas in Lipschitz-Hölder spaces, Rendiconti Lincei Matematica e Applicazioni, 2020
–A., Pirozzi, Toaldo: On the exit time from open sets of some semi-Markov processes, The Annals of Applied Probability, 2020
Some Preprints:
–A., Scalas, Toaldo, Torricelli: Time-changed Markov processes and coupled non-local equations. arXiv preprint arXiv:2412.14956, 2025
–A., Patie, Toaldo: Non-local heat equations with moving boundary. arXiv preprint arXiv:2203.09850, 2025
-Anceschi, A., Castorina, Solombrino: Optimal control problems driven by nonlinear degenerate Fokker-Planck equations, arXiv preprint arXiv:2410.24000, 2024
–A., Ishida, Lőrinczi: Special potentials for relativistic Laplacians I: fractional Rollnik-class, arXiv preprint arXiv:2405.08805, 2024
Books:
–A., Mishura, Pirozzi: Fractional Deterministic and Stochastic Calculus, De Gruyter, 2023
-Angrisani, A., Leone, Mantegazza: Appunti di Calcolo delle Variazioni, Amazon/self published, 2019
Corsi
2024/25
-(MERC area PhD + Bachelor Students): Probability Calculus and Elements of Stochastic Modelling (together with Dr. Graciani Rodrigues)
-(MPHS area PhD): Partial Differential Equations
-(MPHS area PhD): Stochastic Partial Differential Equations
News
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