Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations

Abstract

We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the path ωt on an interval [0, t] becomes the basic variable in the place of classical variables t,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.