2015
DOI: 10.1515/forum-2015-0012
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Regular subspaces of skew product diffusions

Abstract: Abstract. 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 E 1 × E 2 and expressed aswhere X i is a symmetric diffusion on E i for i = 1, 2, and A is a positi… Show more

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Cited by 5 publications
(10 citation statements)
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“…Another proposition states the relation of their global properties. Proposition 2.3 (Remark 3.5, [16]). The following assertions hold.…”
Section: Basic Properties Of Regular Dirichlet Extensionsmentioning
confidence: 96%
See 3 more Smart Citations
“…Another proposition states the relation of their global properties. Proposition 2.3 (Remark 3.5, [16]). The following assertions hold.…”
Section: Basic Properties Of Regular Dirichlet Extensionsmentioning
confidence: 96%
“…In this section, we summarize several basic properties of regular Dirichlet extensions or subspaces, which are contained in [12][13][14][15][16]18]. We always fix two regular Dirichlet forms (E 1 , F 1 ) and (E 2 , F 2 ) on L 2 (E, m) and assume that (E 1 , F 1 ) is a regular Dirichlet subspace of (E 2 , F 2 ), equivalently (E 2 , F 2 ) is a regular Dirichlet extension of (E 1 , F 1 ).…”
Section: Basic Properties Of Regular Dirichlet Extensionsmentioning
confidence: 99%
See 2 more Smart Citations
“…It is shown as the main result of [9] that the state space R of each D-extension of ( 12 D, H 1 (R)) may be essentially decomposed into at most countable invariant intervals and an exceptional set, and on each interval, it behaves as an irreducible diffusion characterized by some appropriate scale function. We refer further explorations about D-subspaces of some other Dirichlet forms to [3,[5][6][7] and [8].…”
Section: Introductionmentioning
confidence: 99%