论文标题
向后双随机微分方程和二次增长的SPDE
Backward doubly stochastic differential equations and SPDEs with quadratic growth
论文作者
论文摘要
在本文中，我们启动了对二次增长的后向后双随机微分方程（BDSDES）的研究。当发电机$ f（t，y，z）$以$ z $四的四边形增长，终端值通过引入一些新想法时，证明了一维BDSDE的存在，比较和稳定性结果。此外，在此框架中，我们使用BDSDE为SOBOLEV空间中半线性随机部分偏微分方程（SPDE）提供了概率表示，并使用它来证明此类SPD的存在和独特性，从而扩展了非线性Feynman-kac公式。
In this paper, we initiate the study of backward doubly stochastic differential equations (BDSDEs, for short) with quadratic growth. The existence, comparison, and stability results for one-dimensional BDSDEs are proved when the generator $f(t,Y,Z)$ grows in $Z$ quadratically and the terminal value is bounded, by introducing some new ideas. Moreover, in this framework, we use BDSDEs to give a probabilistic representation for the solutions of semilinear stochastic partial differential equations (SPDEs, for short) in Sobolev spaces, and use it to prove the existence and uniqueness of such SPDEs, thus extending the nonlinear Feynman-Kac formula.
