English

Weak well-posedness for degenerate SDEs driven by L\'evy processes

Analysis of PDEs 2023-03-27 v3 Probability

Abstract

In this article, we study the effects of the propagation of a non-degenerate L\'evy noise through a chain of deterministic differential equations whose coefficients are H\"older continuous and satisfy a weak H\"ormander-like condition. In particular, we assume some non-degeneracy with respect to the components which transmit the noise. Moreover, we characterize, for some specific dynamics, through suitable counterexamples , the almost sharp regularity exponents that ensure the weak well-posedness for the associated SDE. As a by-product of our approach, we also derive some Krylov-type estimates for the density of the weak solutions of the considered SDE.

Keywords

Cite

@article{arxiv.2107.04325,
  title  = {Weak well-posedness for degenerate SDEs driven by L\'evy processes},
  author = {L. Marino and S. Menozzi},
  journal= {arXiv preprint arXiv:2107.04325},
  year   = {2023}
}

Comments

69 pages. From the previous version, we corrected some typos and added some useful remarks

R2 v1 2026-06-24T04:02:08.997Z