Some theorems on feller processes: Transience, local times and ultracontractivity
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
We present sufficient conditions for the transience and the existence of local times of a Feller process, and the ultracontractivity of the associated Feller semigroup; these conditions are sharp for Lev́y processes. The proof uses a local symmetrization technique and a uniform upper bound for the characteristic function of a Feller process. As a by-product, we obtain for stable-like processes (in the sense of R. Bass) on ℝd with smooth variable index α(x) ∈ (0, 2) a transience criterion in terms of the exponent α(x); if d =1 and infx∈ℝα(x) ∈ (1, 2), then the stable-like process has local times.
Details
Originalsprache | Englisch |
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Seiten (von - bis) | 3255-3286 |
Seitenumfang | 32 |
Fachzeitschrift | Transactions of the American Mathematical Society |
Jahrgang | 365 |
Ausgabenummer | 6 |
Publikationsstatus | Veröffentlicht - 2013 |
Peer-Review-Status | Ja |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- (local) symmetrization, Characteristic function, Feller process, Local time, Stable-like process, Symbol, Transience, Ultracontractivity