论文标题
在弱的Hörmander条件下向后和向前过滤
Backward and forward filtering under the weak Hörmander condition
论文作者
论文摘要
我们为一类变性的部分可观察到的扩散提供了前进和向后滤波方程，满足了弱的Hörmander条件。我们的方法是基于简并SPDE的Hölder理论，该理论允许N. V. Krylov和A. Zatezalo和A. Yu采用直接的方法。 Veretennikov避免使用过滤理论的一般结果。作为副产品，我们还提供了过滤密度的存在，规律性和估计。
We derive the forward and backward filtering equations for a class of degenerate partially observable diffusions, satisfying the weak Hörmander condition. Our approach is based on the Hölder theory for degenerate SPDEs that allows to pursue the direct approaches proposed by N. V. Krylov and A. Zatezalo, and A. Yu. Veretennikov, avoiding the use of general results from filtering theory. As a by-product we also provide existence, regularity and estimates for the filtering density.
