The uniqueness of symmetrizing measure and linear diffusions

Details The uniqueness of symmetrizing measure and linear diffusions The uniqueness of symmetrizing measure and linear diffusions

2009-08-12

arxiv.org/abs/0908.1607v1

Mathematics

Probability

13 papes

Scientific paper

In this short article, we shall study one-dimensional local Dirichlet spaces. One result, which has its independent interest, is to prove that irreducibility implies the uniqueness of symmetrizing measure for right Markov processes. The other result is to give a representation for any 1-dim local, irreducible and regular Dirichlet space and a necessary and sufficient condition for a Dirichlet space to be regular subspace of another Dirichlet space.

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