标题： 拟马尔可夫粘性解的全非线性退化PPDEs 显示英文标题

标题： Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs

摘要： 本文中，我们为全非线性路径依赖型偏微分方程提出了一种新的粘性解类型。通过限制于某种伪马尔可夫结构，我们去除了早期工作中[9, 10]所施加的均匀非退化条件。我们在自然且温和的条件下建立了比较原理。此外，作为应用，我们将结果应用于两类重要的PPDE：由随机优化问题和路径依赖零和博弈问题分别诱导出的随机HJB方程和路径依赖Isaacs方程。 显示英文摘要

摘要： In this paper we propose a new type of viscosity solutions for fully nonlinear path dependent PDEs. By restricting to certain pseudo Markovian structure, we remove the uniform non- degeneracy condition imposed in our earlier works [9, 10]. We establish the comparison principle under natural and mild conditions. Moreover, as applications 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.