From Classical SDEs to Conditional McKean-Vlasov Systems: Theory and Open Problems
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…