Time-dependent diffusion operators on L

被引：9
|
作者：
Stannat, W [1 ]
机构：
[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2004年 / 4卷 / 04期
关键词：
sub-Markovian evolution semigroup; space-time homogenization; infinitesimally invariant measure; generalized Dirichlet forms; diffusion process; martingale problem; Nelson diffusions;
D O I：
10.1007/s00028-004-0147-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Cauchy problem for time-dependent diffusion operators with singular coefficients on L-1-spaces induced by infinitesimal invariant measures. We give sufficient conditions on the coefficients such that the Cauchy-Problem is well-posed. We construct associated diffusion processes with the help of the theory of generalized Dirichlet forms. We apply our results in particular to construct a large class of Nelson-diffusions that could not been constructed before.
引用
收藏
页码：463 / 495
页数：33
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