||WEAK CONVERGENCE OF REGULAR DIRICHLET SUBSPACES
Uemura, Toshihiro ,
Li, LipingYing, Jiangang
Osaka Journal of Mathematics
455 , 2017-07 , Osaka University and Osaka City University, Departments of Mathematics
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 .