The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).


Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some theorems on Feller processes: Transience, local times and ultracontractivity

Authors: René L. Schilling and Jian Wang
Journal: Trans. Amer. Math. Soc. 365 (2013), 3255-3286
MSC (2010): Primary 60J25, 60J75, 35S05
Published electronically: August 21, 2012
MathSciNet review: 3034465
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 Lévy 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 $ \mathbb{R}^d$ with smooth variable index $ \alpha (x)\in (0,2)$ a transience criterion in terms of the exponent $ \alpha (x)$; if $ d=1$ and $ \inf _{x\in \mathbb{R}} \alpha (x)\in (1,2)$, then the stable-like process has local times.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 60J25, 60J75, 35S05

Retrieve articles in all journals with MSC (2010): 60J25, 60J75, 35S05

Additional Information

René L. Schilling
Affiliation: Institut für Mathematische Stochastik, TU Dresden, 01062 Dresden, Germany

Jian Wang
Affiliation: School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People’s Republic of China

Keywords: Feller process, characteristic function, symbol, (local) symmetrization, stable-like process, ultracontractivity, transience, local time
Received by editor(s): August 16, 2011
Received by editor(s) in revised form: October 31, 2011
Published electronically: August 21, 2012
Article copyright: © Copyright 2012 American Mathematical Society

American Mathematical Society