Séminaire de Doctorants : Luca Bondi

Propagation of Chaos for distributional SDEs: A Well-Posedness Result

Propagation of chaos describes the emergence of independence among particles in large stochastic dynamical systems making use of both probabilistic and analytical tools like Stochastic differential equations (SDEs) and partial differential equations (PDEs). The interplay between propagation of chaos, irregular SDEs, and Fokker–Planck PDEs presents a rich framework for understanding complex dynamical systems influenced by randomness. Recent advances have extended the classical theory to systems governed by irregular SDEs, where coefficients lack classical regularity assumptions, posing significant analytical challenges. In this context, irregular SDEs demand novel tools for establishing well-posedness and uniqueness of solutions. This seminar focuses on an introduction of propagation of chaos for SDE  with distributional drift coefficient in the case of additive noise, represented by Brownian motion.