Showing papers by "Shige Peng published in 2016"
TL;DR: In this paper, a path-dependent quasi-linear parabolic PDE was introduced, in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables (t, x) ∈ [ 0, T] × R d, where the terminal values and the generators are allowed to be general function of Brownian motion paths.
Abstract: We introduce a new type of path-dependent quasi-linear parabolic PDEs in which the continuous paths on an interval [0, t] become the basic variables in the place of classical variables (t, x) ∈ [0, T] × R
d
. This new type of PDEs are formulated through a classical BSDE in which the terminal values and the generators are allowed to be general function of Brownian motion paths. In this way, we establish the nonlinear Feynman-Kac formula for a general non-Markovian BSDE. Some main properties of solutions of this new PDEs are also obtained.
100 citations
Posted Content•
TL;DR: In this article, a Stein type characterization for G$-normal distributions is provided, where the expectation of a sublinear expectation is a realization of the expectation associated with the distribution.
Abstract: In this article, we provide a Stein type characterization for $G$-normal distributions: Let $\mathcal{N}[\varphi]=\max_{\mu\in\Theta}\mu[\varphi],\ \varphi\in C_{b,Lip}(\mathbb{R}),$ be a sublinear expectation. $\mathcal{N}$ is $G$-normal if and only if for any $\varphi\in C_b^2(\mathbb{R})$, we have \[\int_\mathbb{R}[\frac{x}{2}\varphi'(x)-G(\varphi"(x))]\mu^\varphi(dx)=0,\] where $\mu^\varphi$ is a realization of $\varphi$ associated with $\mathcal{N}$, i.e., $\mu^\varphi\in \Theta$ and $\mu^\varphi[\varphi]=\mathcal{N}[\varphi]$.