Osaka Journal of Mathematics

Weak convergence of regular Dirichlet subspaces

Abstract

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

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

Dates
First available in Project Euclid: 7 August 2017

https://projecteuclid.org/euclid.ojm/1502092822

Mathematical Reviews number (MathSciNet)
MR3685586

Zentralblatt MATH identifier
1375.31016

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

Citation

Li*, Liping; Uemura, Toshihiro; Ying**, Jiangang. Weak convergence of regular Dirichlet subspaces. Osaka J. Math. 54 (2017), no. 3, 435--455. https://projecteuclid.org/euclid.ojm/1502092822

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