12 citations · 16 across the 4 of their papers we have counts for
4 papers
A priori Holder estimate, parabolic Harnack principle and heat kernel estimates for diffusions with jumps
Zhen-Qing Chen, Takashi Kumagai
In this paper, we consider the following type of non-local (pseudo-differential) operators $\LL $ on : $$ \LL u(x) =\frac12 \sum_{i, j=1}^d \frac{\partial}{\partial x_i} (a_{…
Heat kernel estimates for strongly recurrent random walk on random media
Takashi Kumagai, Jun Misumi
We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are ge…
Convergence of symmetric Markov chains on
R. F. Bass, T. Kumagai, T. Uemura
For each let be a continuous time symmetric Markov chain with state space . A condition in terms of the conductances is given for the convergence of the $Y…
Symmetric jump processes: localization, heat kernels, and convergence
Richard F. Bass, Moritz Kassmann, Takashi Kumagai
We consider symmetric processes of pure jump type. We prove local estimates on the probability of exiting balls, the Hölder continuity of harmonic functions and of heat kernels, an…