Special Session 29: Stochastic Dynamical Systems

Most Probable Paths for McKean--Vlasov Systems: Deriving the Onsager--Machlup Functional via Euler-Type Classical SDEs
Ying Chao
Xi`an Jiaotong University
Peoples Rep of China
Co-Author(s):    
Abstract:
The Onsager--Machlup functional is fundamental in characterizing fluctuations in nonequilibrium systems. For McKean--Vlasov stochastic differential equations, its derivation is challenging due to the distribution dependence in both drift and diffusion terms. In this talk, we introduce an Euler-type approximation scheme based on classical (distribution-independent) stochastic differential equations, each admitting an explicit Onsager--Machlup functional. By proving convergence to the McKean--Vlasov system, we rigorously obtain the corresponding functional in closed form. This constructive approach extends naturally to a broad class of distribution-dependent stochastic systems.