Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients
Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients
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DOI：
10.1016/j.jde.2010.11.021
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
Xicheng Zhang
中科院分区：
文献类型：
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作者：
Xicheng Zhang
本文利用DiPerna - Lions理论（DiPerna and Lions, 1989）[1]，研究了具有无界和退化非光滑系数的线性二阶随机偏微分方程，得到了其存在唯一性的若干条件。此外，我们还证明了SPDEs广义解的l1可积性和一般极大原理。作为应用，我们研究了非线性滤波问题，并得到了一类退化非线性SPDE广义解的存在唯一性。
In this article, using DiPerna–Lions theory (DiPerna and Lions, 1989) [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1-integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinear filtering problem and also obtain the existence and uniqueness of generalized solutions for a degenerate nonlinear SPDE.