3 papers
math.PR2025
Smooth measures and positive continuous additive functionals attached to a compact nest
Takumu Ooi, Kaneharu Tsuchida, Toshihiro Uemura
The relationship between smooth measures and positive continuous additive functionals is well known, and this correspondence is called the Revuz correspondence. We investigate the…
math.PR2022
Markov properties for Gaussian fields associated with Dirichlet forms
Takumu Ooi
We prove the equivalence of the local property for an irreducible regular Dirichlet form and the Markov property for the Gaussian field associated with the Dirichlet form. Moreover…
math.PR2020
Heat kernel estimates on spaces with varying dimension
Takumu Ooi
We obtain sharp two-sided heat kernel estimates on spaces with varying dimension, in which two spaces of general dimension are connected at one point. On these spaces, if the dimen…