Regularity of Invariant Measures: The Case of Non-constant Diffusion Part
Regularity of Invariant Measures: The Case of Non-constant Diffusion Part
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DOI：
10.1006/jfan.1996.0063
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发表时间：
1996-05
影响因子：
1.7
通讯作者：
V. Bogachev;N. Krylov;M. Röckner
中科院分区：
文献类型：
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作者：
V. Bogachev;N. Krylov;M. Röckner
证明了Rd上的测度μ满足方程L*μ=0的正则性(即光滑性)，其中L是一类算子Lu=tr(au“)+B·∇u.这里A是Lipschitz连续的一致椭圆矩阵值映射，B仅是μ平方可积的.我们还处理了一类相应的无限维情形，其中RD被局部凸拓扑向量SpaceX所代替。在这种情况下，证明了μ是绝对连续的。X上的高斯测度和Radon-Nikodym密度的平方根属于Malliavin检验函数空间D2，1。
We prove regularity (i.e., smoothness) of measuresμon Rdsatisfying the equationL*μ=0 whereLis an operator of typeLu=tr(Au″)+B·∇u. HereAis a Lipschitz continuous, uniformly elliptic matrix-valued map andBis merelyμ-square integrable. We also treat a class of corresponding infinite dimensional cases where Rdis replaced by a locally convex topological vector spaceX. In this casesμis proved to be absolutely continuous w.r.t. a Gaussian measure onXand the square root of the Radon–Nikodym density belongs to the Malliavin test function space D2, 1.