7 papers
Energy integrals and asymmetric co-potentials for closed forms
Kazuhiro Kuwae, Takumu Ooi, Kaneharu Tsuchida +1
We investigate the class of measures of finite energy integrals and the behavior of potentials and co-potentials associated with non-symmetric closed forms. In particular, we compa…
Classification and Metrization of Classes of Smooth measures
Takumu Ooi, Kaneharu Tsuchida, Toshihiro Uemura
We classify the several classes of the set of smooth measures from the perspective of the denseness and the locality, and consider their relationships, in particular, that of the K…
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…
Convergence of processes time-changed by Gaussian multiplicative chaos
Takumu Ooi
As represented by the Liouville measure, Gaussian multiplicative chaos is a random measure constructed from a Gaussian field. Under certain technical assumptions, we prove the conv…
Dynkin games for Markov processes associated with semi-Dirichlet forms
Takumu Ooi, Toshihiro Uemura
We consider Dynkin games for Markov processes associated with semi-Dirichlet forms. Dynkin games are the optimal stopping games introduced as the models of zero-sum games by two pl…
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…
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…