Existence and Comparisons for BSDEs in general spaces
Existence and Comparisons for BSDEs in general spaces
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DOI：
10.1214/11-aop679
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发表时间：
2010-01
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影响因子：
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通讯作者：
Samuel N. Cohen;R. Elliott
中科院分区：
文献类型：
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作者：
Samuel N. Cohen;R. Elliott
本文给出了连续时间中任意过滤概率空间的倒向随机微分方程的理论。没有假设是关于连续性的过滤，或可预测的二次变化的鞅在这个空间。我们提出的平方可积解的存在性和唯一性的条件，使用Lipschitz连续的驱动程序。这些条件统一了连续时间和离散时间中存在的要求，并允许离散过程嵌入连续过程。我们还提出了一个比较定理的条件，从而在这些一般空间中构造时间一致的非线性期望。MSC分类：60H20、60H10、91B16
We present a theory of Backward Stochastic Differential Equations in continuous time with an arbitrary filtered probability space. No assumptions are made regarding the continuity of the filtration, or of the predictable quadratic variations of martingales in this space. We present conditions for existence and uniqueness of square-integrable solutions, using Lipschitz continuity of the driver. These conditions unite the requirements for existence in continuous and discrete time, and allow discrete processes to be embedded with continuous ones. We also present conditions for a comparison theorem, and hence construct time consistent nonlinear expectations in these general spaces. MSC Classification: 60H20, 60H10, 91B16