Related papers: Discrete approximation of semi-Dirichlet forms wit…

We study the convergence of resistance metrics and resistance forms on a converging sequence of spaces. As an application, we study the existence and uniqueness of self-similar Dirichlet forms on Sierpinski gaskets with added rotated…

We develop sufficient analytic conditions for conservativeness of non-sectorial perturbations of symmetric Dirichlet forms which can be represented through a carr\'e du champ on a locally compact separable metric space. These form an…

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a…

This thesis is about local and non-local Dirichlet forms on the Sierpi\'nski gasket and the Sierpi\'nski carpet. We are concerned with the following three problems in analysis on the Sierpi\'nski gasket and the Sierpi\'nski carpet. First, a…

We prove that stable-like non-local Dirichlet forms converge to local Dirichlet form in the sense of Mosco on metric measure spaces. We prove that subordinated Dirichlet forms converge to the original Dirichlet form in the sense of Mosco on…

We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli…

We elaborate a new method for constructing traces of quadratic forms in the framework of Hilbert and Dirichlet spaces. Our method relies on monotone convergence of quadratic forms and the canonical decomposition into regular and singular…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which…

We obtain a criterion for the quasi-regularity of generalized (non-sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasi-regularity of (sectorial) semi-Dirichlet forms. Given the right (Markov) process…

By using the analytic tools of Dirichlet forms, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along a fractal (which can be considered as a simplified rough porous…

We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to…

We give sufficient conditions for Mosco convergences for the following three cases: symmetric locally uniformly elliptic diffusions, symmetric L\'evy processes, and symmetric jump processes in terms of the $L^1(\mathbb R;dx)$-local…

In this paper we discuss weak convergence of continuous-time Markov chains to a non-symmetric pure jump process. We approach this problem using Dirichlet forms as well as semimartingales. As an application, we discuss how to approximate a…

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…

We provide decompositions of Dirichlet forms into recurrent and transient parts as well as into conservative and dissipative parts, in the framework of Hausdorff state spaces. Combining both formulae we write every Dirichlet form as the sum…

We construct a self-similar local regular Dirichlet form on the Sierpi\'nski gasket using $\Gamma$-convergence of stable-like non-local closed forms. As a continuation of a recent paper by Grigor'yan and the author, we give the first…

We comment on the discretization of the Dirac equation using finite element spaces of differential forms. In order to treat perturbations by low order terms, such as those arizing from electromagnetic fields, we develop some abstract…

This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…