Title: A Sample Path Large Deviation Principle for a class of path-dependent Mean-field Forward-Backward SDEs with vanishing Common noise (starts 9.00 sharp)
Abstract: I will review a recent result on a sample path large deviation principle (LDP) for path-dependent forward-backward Stochastic Differential Equations (FBSDE) of mean-field type with vanishing common noise.
This is achieved through the Laplace Principle, obtained from a variational representation of the scaled free-energy process in terms of solutions to quadratic backward SDEs. The method bypasses the contraction principle applied so far to standard Markov FBSDEs by using the connection between BSDEs, driven by Markov forward diffusions, with viscosity solutions to semilinear parabolic PDEs.
