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Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients

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  • Marino, L.
  • Menozzi, S.

Abstract

In this article, we study the effects of the propagation of a non-degenerate Lévy noise through a chain of deterministic differential equations whose coefficients are Hölder continuous and satisfy a weak Hörmander-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 counter-examples, 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.

Suggested Citation

  • Marino, L. & Menozzi, S., 2023. "Weak well-posedness for a class of degenerate Lévy-driven SDEs with Hölder continuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 106-170.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:106-170
    DOI: 10.1016/j.spa.2023.04.012
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    References listed on IDEAS

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    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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