BDSDEs with locally monotone coefficients and Sobolev solutions for SPDEs
BDSDEs with locally monotone coefficients and Sobolev solutions for SPDEs
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DOI：
10.1016/j.jde.2011.05.017
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发表时间：
2011-08
影响因子：
2.4
通讯作者：
Zhen Wu;Feng Zhang
中科院分区：
文献类型：
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作者：
Zhen Wu;Feng Zhang
In this paper, we obtain the existence and uniqueness result of the solutions to backward doubly stochastic differential equations (BDSDEs for short) with locally monotone coefficients. As an intermediate step, we also obtain an existence and uniqueness result for the solutions to BDSDEs with one kind of globally monotone coefficients. And then we give the probabilistic interpretation for the solutions in Sobolev spaces of quasilinear stochastic partial differential equations (SPDEs for short) in terms of these two classes of BDSDEs.
