带二次增长的半线性抛物型PDE Sobolev解的概率表示（英文）

Probabilistic Interpretation for Sobolev Solution of Semilinear Parabolic PDE with Quadratic Growth Coefficient

本文讨论一类带有二次增长系数的半线性抛物型偏微分方程,通过一个倒向随机微分方程,作者证明该偏微分方程Sobolev解的存在唯一性,并且还给出Sobolev解的概率表示.主要方法是使用压缩映射原理和随机流技巧.

In this paper,we study a class of semilinear parabolic PDE with quadratic growth coefficient.By using a backward stochastic differential equation,we prove the existence and uniqueness result for Sobolev solution.Moreover,we give a probabilistic interpretation for the Sobolev solution.The main methods are using contraction mapping principle and stochastic flow technics.