Osaka Journal of Mathematics

Weak convergence of regular Dirichlet subspaces

Liping Li*, Toshihiro Uemura, and Jiangang Ying**

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In this paper we shall prove the weak convergence of the associated diffusion processes of regular subspaces with monotone characteristic sets for a fixed Dirichlet form. More precisely, given a fixed 1-dimensional diffusion process and a sequence of its regular subspaces, if the characteristic sets of regular subspaces are decreasing or increasing, then their associated diffusion processes are weakly convergent to another diffusion process. This is an extended result of [14].

Article information

Osaka J. Math., Volume 54, Number 3 (2017), 435-455.

First available in Project Euclid: 7 August 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 31C25: Dirichlet spaces
Secondary: 60F05: Central limit and other weak theorems


Li*, Liping; Uemura, Toshihiro; Ying**, Jiangang. Weak convergence of regular Dirichlet subspaces. Osaka J. Math. 54 (2017), no. 3, 435--455.

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