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

@article{Schilling2011SomeTO,
  title={Some theorems on Feller processes: transience, local times and ultracontractivity},
  author={R. Schilling and J. Wang},
  journal={Transactions of the American Mathematical Society},
  year={2011},
  volume={365},
  pages={3255-3286}
}
  • R. Schilling, J. Wang
  • Published 2011
  • Mathematics
  • Transactions of the American Mathematical Society
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 Levy 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… Expand
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