Abstract
For a Markov process associated with a not necessarily symmetric regular Dirichlet form, if the form satisfies the sector condition, then any semipolar sets are exceptional. On the other hand, in the case of the space-time Markov process associated with a family of time dependent Dirichlet forms, there exist non-exceptional semipolar sets. The main purpose of this paper is to show that any semipolar set $B=J\times \Gamma$ of the direct product type of a subset $J$ of time and a subset $\Gamma$ of space is exceptional if $J$ has positive Lebesgue measure.
Citation
Yoichi Oshima. "On the exceptionality of some semipolar sets of time inhomogeneous Markov processes." Tohoku Math. J. (2) 54 (3) 443 - 449, 2002. https://doi.org/10.2748/tmj/1113247604
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