Osaka Journal of Mathematics

On regular Dirichlet subspaces of $H^{1}(I)$ and associated linear diffusions

Abstract

We will give a complete characterization of all regular Dirichlet subspaces of $H^1(I)$ for a finite open interval $I$ by a certain family of scale functions. Each associated diffusion will be constructed from a reflecting Brownian motion on a closed interval by a time change and a transformation of the state space.

Article information

Source
Osaka J. Math., Volume 42, Number 1 (2005), 27-41.

Dates
First available in Project Euclid: 21 July 2006

Fang, Xing; Fukushima, Masatoshi; Ying, Jiangang. On regular Dirichlet subspaces of $H^{1}(I)$ and associated linear diffusions. Osaka J. Math. 42 (2005), no. 1, 27--41. https://projecteuclid.org/euclid.ojm/1153494313