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

页码：463 / 495

页数：33

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