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math.AP2015★ 3 cited
Comparison of viscosity solutions of fully nonlinear degenerate parabolic Path-dependent PDEs
Zhenjie Ren, Nizar Touzi, Jianfeng Zhang
We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi &…
math.AP2014★ 1 cited
An overview of Viscosity Solutions of Path-Dependent PDEs
Zhenjie Ren, Nizar Touzi, Jianfeng Zhang
This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall-…
math.AP2014★ 8 cited
Viscosity Solutions of Fully Nonlinear Elliptic Path Dependent PDEs
Zhenjie Ren
This paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type a…