Schauder Estimates for Poisson Equations Associated with Non-local Feller Generators
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
We show how Hölder estimates for Feller semigroups can be used to obtain regularity results for solutions to the Poisson equation Af= g associated with the (extended) infinitesimal generator of a Feller process. The regularity of f is described in terms of Hölder–Zygmund spaces of variable order and, moreover, we establish Schauder estimates. Since Hölder estimates for Feller semigroups have been intensively studied in the last years, our results apply to a wide class of Feller processes, e.g. random time changes of Lévy processes and solutions to Lévy-driven stochastic differential equations. Most prominently, we establish Schauder estimates for the Poisson equation associated with the fractional Laplacian of variable order. As a by-product, we obtain new regularity estimates for semigroups associated with stable-like processes.
Details
Original language | English |
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Pages (from-to) | 1506-1578 |
Number of pages | 73 |
Journal | Journal of Theoretical Probability |
Volume | 34 |
Issue number | 3 |
Publication status | Published - Sept 2021 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- Favard space, Feller process, Hölder space of variable order, Infinitesimal generator, Regularity