Stochastic flows and the C0-diffusion property
Stochastic flows and the C0-diffusion property
复制标题
随机流和 C0 扩散特性
DOI：
10.1080/17442508208833205
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发表时间：
1982
影响因子：
1.1
通讯作者：
K. Elworthy
中科院分区：
文献类型：
--
作者：
K. Elworthy
用一个基本论证来表明，具有由微分同胚组成的流的随机动力系统的马尔可夫半群必然保留无穷大消失的连续函数的空间。在一维情况下，这被视为也是一个充分条件。作为推论，Kunita 在稍强的系数条件下证明了一个结果：R 上的非简并系统具有由同胚组成的流，当且仅当 ± ∞ 都是自然边界时。
An elementary argument is used to show that the Markov semigroup of a stochastic dynamical system which has a flow consisting of diffeomorphisms necessarily preserves the space of continuous functions vanishing at infinity. In the one dimensional case this is seen to be also a sufficient condition. As a corollary there is a result proved by Kunita under slightly stronger conditions on the coefficients: a non-degenerate system on R has a flow consisting of homeomorphisms if and only if both ± ∞ are natural boundaries.