Heat kernel estimates for Markov processes of direction-dependent type
Probability
2024-04-12 v2 Analysis of PDEs
Abstract
We prove sharp pointwise heat kernel estimates for symmetric Markov processes associated with symmetric Dirichlet forms that are local with respect to some coordinates and nonlocal with respect to the remaining coordinates. The main theorem is a robustness result like the famous estimate for the fundamental solution of second order differential operators, obtained by Donald G. Aronson. Analogous to his result, we show that the corresponding translation-invariant process and the one given by the general Dirichlet form share the same pointwise points.
Cite
@article{arxiv.2106.07282,
title = {Heat kernel estimates for Markov processes of direction-dependent type},
author = {Jaehoon Kang and Moritz Kassmann},
journal= {arXiv preprint arXiv:2106.07282},
year = {2024}
}