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Hunt's hypothesis and symmetrization for general 1-dimensional diffusions
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In this paper, we will consider the problem that how far from Hunt's hypothesis (H) to symmetrization for a general 1-dimensional diffusion. A characterization of (H) involving the classification of points for this diffusion will be first obtained. Then the main result shows that such a process is symmetrizable, if and only if (H) holds and a certain family of asymmetric shunt points is empty. Furthermore, we will also derive the representation of associated Dirichlet forms of general 1-dimensional diffusions under symmetry.
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