Schauder Estimates for Poisson Equations Associated with Non-local Feller Generators

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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

OriginalspracheEnglisch
Seiten (von - bis)1506-1578
Seitenumfang73
FachzeitschriftJournal of Theoretical Probability
Jahrgang34
Ausgabenummer3
PublikationsstatusVeröffentlicht - Sept. 2021
Peer-Review-StatusJa

Schlagworte

Schlagwörter

  • Favard space, Feller process, Hölder space of variable order, Infinitesimal generator, Regularity