Kolmogorov Operators and Their Applications

Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.

This volume collects a selection of the talks given at the Cortona meeting by experts in both fields, who presented the most recent developments of the theory. Particular emphasis has been given to degenerate partial differential equations, Itô processes, applications to kinetic theory and to finance.

Stéphane Menozzi is Full Professor at Université d’Évry Val d’Essonne-Paris Saclay. His research concerns degenerate and/or singular Stochastic Differential Equations, regularity, heat-kernel estimates, approximation. Those equations can be viewed as the probabilistic counterpart to the corresponding Kolmogorov operators.

Andrea Pascucci is Full Professor of Probability and Statistics at the Alma Mater Studiorum - Università di Bologna. His expertise lies in Stochastic Partial Differential Equations, particularly of degenerate parabolic type. He has contributed to the field, focusing on applications in mathematical finance, including American options, Asian/path-dependent options, and volatility modeling.

Sergio Polidoro is Full professor of Mathematical Analysis at the University of Modena and Reggio Emilia. His research activity mainly concerns regularity theory for second order partial differential equations with non-negative characteristic form. His main contributions in this field are regularity results and heat-kernel estimates for degenerate Kolmogorov equations.