In this paper, we propose a new type of viscosity solutions for fully nonlinear path-dependent PDEs. By restricting the solution to a pseudo-Markovian structure defined below, we remove the uniform non-degeneracy condition needed in our earlier works (Ekren, I, Touzi, N, Zhang, J, Ann Probab, 44:1212–1253, 2016a; Ekren, I, Touzi, N, Zhang, J, Ann Probab, 44:2507–2553, 2016b) to establish the uniqueness result. We establish the comparison principle under natural and mild conditions. Moreover, we apply our results to two important classes of PPDEs: the stochastic HJB equations and the path-dependent Isaacs equations, induced from the stochastic optimization with random coefficients and the path-dependent zero-sum game problem, respectively.

中文翻译：

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完全非线性简并PPDEs的伪马尔可夫粘度解

在本文中，我们为完全非线性的路径依赖的PDE提出了一种新型的粘度解决方案。通过将解决方案限制为以下定义的伪马尔可夫结构，我们消除了我们早期工作中所需的一致的非简并性条件（Ekren，I，Touzi，N，Zhang，J，Ann Probab，44：1212–1253，2016a; Ekren，I，Touzi，N，Zhang，J，Ann Probab，44：2507–2553，2016b）建立唯一性结果。我们建立了自然和温和条件下的比较原理。此外，我们将结果应用于两类重要的PPDE：分别由随机系数的随机优化和与路径相关的零和博弈问题引起的随机HJB方程和与路径相关的Isaacs方程。