|
Session 25. Nonlocal Phenomena: Levy processes and related operators
|
Intrinsic scaling properties of jump processes |
Moritz Kassmann, Bielefeld University, Germany
|
The talk is based on the joint work with Ante Mimica.
|
|
|
Scaling properties play a fundamental role for many reasons. Often, a scaling
property is characterised by a real number, e.g. the index of stability when
studying stable processes. In the talk we study phenomena where this is not
possible, e.g. the exit time estimates of geometric stable processes. These
estimates are applied to questions of regularity for generators of Markov
processes and growth lemmas for corresponding integro-differential equations.
The generators are allowed to have an arbitrary order of
differentiability less than \(2\). We explain that, in general, this order is
represented by a function and not by a number. Our approach enables a
careful study of regularity issues up to the phase boundary between
integro-differential (positive order of differentiability) and integral
operators (no differentiability).
|
|
| Print version |
|
