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 ${\omega }_t$ on an interval [0, $t$] becomes the basic variable in the place of classical variables $\left(t,x\right)\in [0,T]\times {ℝ}^d$. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.