On viscosity solutions of path dependent PDEs
On viscosity solutions of path dependent PDEs
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DOI：
10.1214/12-aop788
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发表时间：
2011-09
影响因子：
2.3
通讯作者：
Ibrahim Ekren;C. Keller;N. Touzi;Jianfeng Zhang
中科院分区：
文献类型：
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作者：
Ibrahim Ekren;C. Keller;N. Touzi;Jianfeng Zhang
在本文中，我们提出了路径依赖的半线性抛物型偏微分方程粘性解的概念。这也可以看作是非马尔可夫倒向随机微分方程的粘性解，从而将著名的非线性Feynman-Kac公式推广到非马尔可夫情形。我们将证明粘性解的存在性、唯一性、稳定性和比较原理。我们的方法的关键组成部分是一个功能的It^ o的演算最近介绍了Dupire [6]。
In this paper we propose a notion of viscosity solutions for path dependent semilinear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian Backward SDEs, and thus extends the well known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability, and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional It^ o’s calculus recently introduced by Dupire [6].