Hunt's hypothesis and symmetrization for general 1-dimensional diffusions

2021/07/13 by Li, Liping
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2107.06163

Abstract

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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