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}
}
  • Liping Li, J. Ying
  • Published 2 June 2016
  • Mathematics
  • Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
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… 

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