Abstract:
This talk presents a structured overview of stochastic differential equations (SDEs), beginning with classical Itô diffusions and progressively incorporating jumps, regime switching, and interacting particle systems. We then introduce McKean—Vlasov equations, where the dynamics depend on the law of the solution itself, highlighting their nonlinear and mean-field nature. Particular emphasis is placed on conditional McKean—Vlasov systems, in which the coefficients depend on conditional distributions relative to a given filtration. These models naturally arise in problems involving partial information, systemic risk, common noise, and interacting agents under uncertainty. After revisiting classical Itô diffusions and mean-field limits, we extend the framework to jump-diffusion models driven by compensated Poisson random measures and to hybrid systems with finite-state Markovian switching. We discuss propagation of chaos, well-posedness, analytical challenges, and connections with associated nonlocal partial differential equations . The talk concludes with several open problems, including regularity issues, numerical approximation schemes and others.
Place: Monzón 201
Hour: 10:30 a.m.