Conditional Propagation of Chaos and a Class of Quasilinear PDE'S

Abstract

We consider conditional propagation of chaos and use it to solve a class of quasilinear equations of parabolic type. In addition, we construct a class of continuous stochastic processes associated with the above nonlinear equations. Our method imposes fewer smoothness conditions on the coefficients and allows a degenerate nonlinear weight before a divergence form operator. We hope this probabilistic approach will introduce a better microscopic picture for understanding some Stefan type problems.