The partial malliavin calculus and its application to non-linear filtering
The partial malliavin calculus and its application to non-linear filtering
复制标题
偏马利亚文微积分及其在非线性滤波中的应用
DOI：
10.1080/17442508408833296
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发表时间：
1984
影响因子：
2
通讯作者：
D. Stroock
中科院分区：
文献类型：
--
作者：
S. Kusuoka;D. Stroock
在本文中，使用 Malliavin 微积分推导给定第二个 Ito 过程的一个 ltd 过程的条件分布的正则性质。所涉及的过程之间的关系是过滤理论研究中通常假设的关系。我们要求的非简并性是用定理（3.15）中的 Malliavins 协方差矩阵来表示的。对于一般 Tto 过程，引理 (3.19) 和扩散引理 (3.29) 给出了更实际的条件。最后，在定理（4.6）中，给出了这些结果的“局部”版本用于扩散。
In this article, the Malliavin calculus is used to derive regularity properties of the conditional distribution of one ltd process given a second Ito process. The relation between the processes involved is the usual one assumed in the study of filtering theory. The non-degeneracy which we require is stated in terms of Malliavins covariance matrix in Theorem (3.15). More practical conditions are given in Lemma (3.19) for general Tto processes and in Lemma (3.29) for diffusions. Finally, in Theorem (4.6) a “localized” version of these results is given for diffusions.