2015/04/20 by Liping Li, Li, Liping, Jiangang Ying +1
Computer Science · Mathematics · #31C25 #60J55 #60J60 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #math.PR #msc:31C25 #msc:60J55 #msc:60J60
paper · pdf · doi:10.48550/arxiv.1504.04981
openalex publication_date 2015/04/20 · arxiv created 2015/06/18 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Roughly speaking, the regular subspace of a Dirichlet form is also a regular Dirichlet form on the same state space. It inherits the same form of original Dirichlet form but possesses a smaller domain. What we are concerned in this paper are the regular subspaces of associated Dirichlet forms of skew product diffusions. A skew product diffusion X is a symmetric Markov process on the product state space E1× E2 and expressed as Xt=(X1t,X2At), t≥ 0, where Xi is a symmetric diffusion on Ei for i=1,2, and A is a positive continuous additive functional of X1. One of our main results indicates that any skew product type regular subspace of X, say Yt=(Y1t,Y2_At), t≥ 0, can be characterized as follows: the associated smooth measure of A is equal to that of A, and Yi corresponds to a regular subspace of Xi for i=1,2. Furthermore, we shall make some discussions on rotationally invariant diffusions on Rd∖ \0\, which are special skew product diffusions on (0,∞)× Sd-1. Our main purpose is to extend a regular subspace of rotationally invariant diffusion on Rd∖ \0\ to a new regular Dirichlet form on Rd.