5 papers · 1 filter
A simplified characterization of stable-like heat kernel estimates
Mathav Murugan
We study heat kernel estimates for symmetric pure jump processes on general metric measure spaces. Building on recent progress in the local setting due to S.~Eriksson-Bique, we dev…
Diffusions and random walks with prescribed sub-Gaussian heat kernel estimates
Mathav Murugan
Given suitable functions , we obtain necessary and sufficient conditions on for the existence of a metric measure space and a symmetric diff…
On the energy image density conjecture of Bouleau and Hirsch
Sylvester Eriksson-Bique, Mathav Murugan
We affirmatively resolve the energy image density conjecture of Bouleau and Hirsch (1986). Beyond the original framework of Dirichlet structures, we establish the energy image dens…
Martingale and analytic dimensions coincide under Gaussian heat kernel bounds
Mathav Murugan
Given a strongly local Dirichlet form on a metric measure space that satisfies Gaussian heat kernel bounds, we show that the martingale dimension of the associated diffusion proces…
Heat kernel estimates for boundary traces of reflected diffusions on uniform domains
Naotaka Kajino, Mathav Murugan
We study the boundary trace processes of reflected diffusions on uniform domains. We obtain stable-like heat kernel estimates for such a boundary trace process when the diffusion o…