Some theorems on Feller processes: Transience, local times and ultracontractivity
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- by René L. Schilling and Jian Wang PDF
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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
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Additional Information
- René L. Schilling
- Affiliation: Institut für Mathematische Stochastik, TU Dresden, 01062 Dresden, Germany
- Email: rene.schilling@tu-dresden.de
- Jian Wang
- Affiliation: School of Mathematics and Computer Science, Fujian Normal University, 350007, Fuzhou, People’s Republic of China
- Email: jianwang@fjnu.edu.cn
- Received by editor(s): August 16, 2011
- Received by editor(s) in revised form: October 31, 2011
- Published electronically: August 21, 2012
- © Copyright 2012 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 3255-3286
- MSC (2010): Primary 60J25, 60J75, 35S05
- DOI: https://doi.org/10.1090/S0002-9947-2012-05738-2
- MathSciNet review: 3034465