orcidId:0000-0002-1437-2054

I am a PhD student since October 2018 under the supervision of Stéphane Menozzi (Université d'Évry Val d’Essonne - Paris Saclay) and Enrico Priola (Università degli studi di Pavia).
My thesis is dedicated to study phenomena restoring uniqueness for some ill-posed ODEs. The idea is to perturb the dynamics by a noise acting only on some components of the ODE and propagating through the other ones thanks to a weak Hörmander like condition, as in the framework of Kolmogorov degeneracy. The noise we consider is a jump Lévy process (integro-differential framework for the generator of the noise). We are particularly interested in the minimal regularity assumptions on the coefficients leading to the weak well-posedness of the associated SDE. As an application, we apply our method to a Hamiltonian model arising from a mechanical problem involving friction.

• Stochastic Analysis: Regularization by Noise, Degenerate systems, Lévy jump noises
• PDE techniques: A priori Estimates, Schauder Estimates, Well-posedness for Integro-Partial Differential equations

• L. Marino, S. Menozzi, E. Priola Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators (2021). ArXiv Preprint.
  
• L. Marino, S. Menozzi, Weak well-posedness for degenerate SDEs driven by Lévy processes (2021). ArXiv Preprint.
  
• L. Marino, Schauder estimates for degenerate Lévy Ornstein-Uhlenbeck operators. Journal of Mathematical Analysis and Applications, 500(1):125168, 37 pp., 2021.
  
• L. Marino, Schauder estimates for degenerate stable Kolmogorov equations. Bulletin des Sciences Mathématiques, 162:102885, 98 pp., 2020.
  

• Potential Theory and Hypocoercivity Approaches for Kinetic Equations (Università di Modena e Reggio Emilia) 2 February 2021 : Schauder estimates for degenerate Lévy Kolmogorov equations.
  
• Se mi Narri di Matematica, PhD workshop (Università di Pavia) 24 April 2020 : Better if Random! An introduction to the regularization by noise.
  
• LSA Winter Meeting 2019 (Higher school of Economics (HSE), Moscow) 6 December 2019 : Weak well-posedness for a class of degenerate SDEs driven by stable processes.
  
• Second Italian Meeting on Probability and Mathematical Statistics (Vietri sul Mare, Italy) 20 June 2019 : Weak well-posedness for degenerate SDEs driven by stable processes.
  
• Perturbation Techniques in Stochastic Analysis and Its Applications (Centre International de Rencontres Mathematiques (CIRM), Marseille) 15 March 2019 : Schauder estimates for degenerate stable Ornstein-Uhlenbeck operators.
  

• Master thesis “Transport Equations with Low Regularity Vector Fields” under the supervision of Xue-Mei Li (Warwick University) Master Thesis
  
• Bachelor Thesis “Disintegration Theorem and its Application to Conditional Probabilities” under the supervision of Ernesto De Vito (Università di Genova) Bachelor Thesis
  

• 2020-2021 : Teaching assistant for Mathematics and Statistics, department of Biology and Biotechnology, Università di Pavia.
  
• 2019-2020 : Teaching assistant for Mathematical Analysis 2, department of Civil Engineering and Architecture, Università di Pavia.
  
• 2019-2020 : Teaching assistant for Complements of Mathematical Analysis and Statistics, department of Industrial Engineering, Università di Pavia.
  
• 2018-2019 : Teaching assistant for Analysis 1, Algebra 1, Linear Algebra and Analytic Geometry, department of Mathematics, Università di Genova.