|Location:||MSRI: Simons Auditorium, Online/Virtual|
Jump Diffusions On Metric Measure Spaces
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Symmetric jump diffusions can be characterized by their non-local DIrichlet forms. In this talk, we consider symmetric non-local Dirichlet forms on metric measure spaces under general volume doubling condition, and study the stability of heat kernel estimates bounds and parabolic Harnack inequalities under bounded perturbations. We will present their stable equivalent characterizations in terms of the jumping kernels, variants of cut-off Sobolev inequalities, the
Faber-Krahn inequalities and Poincare inequalities. In particular, we establish the stability of heat kernel estimates for \alpha-stable-like processes even with \alpha greater than 2 when the underlying spaces have walk dimensions larger than 2. The connection between parabolic Harnack inequalities and two-sided heat kernel estimates, as well as with the Holder regularity of parabolic functions for symmetric non-local Dirichlet forms will also be given.
Based on joint works with T. Kumagai and J. Wang.
Jump Diffusions on Metric Measure Spaces