My research interests lie at the interface between probability and PDEs and their applications to physics or finance, with particular focus on models which involve Lévy-type processes or integro-partial differential operators. More precisely:
Regularisation by noise: SDEs driven by anomalous noise, e.g. degenerate and/or Lévy processes;
Regularity theory for evolution equation: Schauder estimates, Sobolev estimates, Hypoelliptic equations;
Stochastic homogenisation: homogenisation of integro-differential operators in random environments, diffusive scaling limits of linear Boltzmann equations.
You can also find me on arXiv, Google Scholar, Mathscinet, ORCID and ResearchGate.
Klimsiak, Komorowski, Marino. Homogenization of stable-like operators with random, ergodic coefficients. Journal of Differential Equations, 10.1016/j.jde.2025.02.054, 2025.
Marino, Menozzi, Priola. About the regularity of degenerate non-local Kolmogorov operators under diffusive perturbations. Proceedings of INdAM Meeting ”Kolmogorov Operators and their applications”, Springer INdAM series,10.1007/978-981-97-0225-1_8, 2024.
Bogdan, Komorowski, Marino. Anomalous diffusion limit for a kinetic equation with a thermostatted interface. Probability Theory and related Fields, 0.1007/s00440-023-01251-3, 2023.
Marino, Menozzi. Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients. Stochastic Processes and their applications, 10.1016/j.spa.2023.04.012, 2023.
Marino, Menozzi, Priola. Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators. Studia Mathematica, 10.4064/sm210819-13-4, 2022.
Marino. Schauder estimates for degenerate Lévy Ornstein-Uhlenbeck operators. Journal of Mathematical Analysis and Applications, 500(1):125168, 2021.
Marino. Schauder estimates for degenerate stable Kolmogorov equations. Bulletin des Sciences Mathématiques, 162:102885, 98, 2020.
2021 - Ph.D. thesis: Weak regularisation by degenerate Lévy noise and its applications.
Supervisor: Stéphane Menozzi (Université Paris-Saclay) and Enrico Priola (Università degli studi di Pavia).
2017 - Master thesis: Transport equations with low regularity vector fields.
Supervisor: Xue-Mei Li (Warwick University).
2016 - Bachelor thesis: Disintegration theorem and its application to conditional probabilities.
Supervisor: Ernesto De Vito (Università di Genova).