English

Transition probabilities of L\'evy-type processes: Parametrix construction

Probability 2019-02-18 v2

Abstract

We present an existence result for L\'evy-type processes which requires only weak regularity assumptions on the symbol q(x,ξ)q(x,\xi) with respect to the space variable xx. Applications range from existence and uniqueness results for L\'evy-driven SDEs with H\"older continuous coefficients to existence results for stable-like processes and L\'evy-type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of L\'evy and L\'evy-type processes. The paper includes an extensive list of L\'evy(-type) processes satisfying the assumptions of our results.

Keywords

Cite

@article{arxiv.1702.00778,
  title  = {Transition probabilities of L\'evy-type processes: Parametrix construction},
  author = {Franziska Kühn},
  journal= {arXiv preprint arXiv:1702.00778},
  year   = {2019}
}
R2 v1 2026-06-22T18:07:58.403Z