# Regular Dirichlet extensions of one-dimensional Brownian motion

@article{Li2019RegularDE, title={Regular Dirichlet extensions of one-dimensional Brownian motion}, author={Liping Li and Jiangang Ying}, journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques}, year={2019} }

The regular Dirichlet extension is the dual concept of regular Dirichlet subspace. The main purpose of this paper is to characterize all the regular Dirichlet extensions of one-dimensional Brownian motion and to explore their structures. It is shown that every regular Dirichlet extension of one-dimensional Brownian motion may essentially decomposed into at most countable disjoint invariant intervals and an $\mathcal{E}$-polar set relative to this regular Dirichlet extension. On each invariant…

## 8 Citations

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