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

L. Marino and S. Menozzi

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 106-170

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.

Keywords: Degenerate Lévy driven SDEs; Well-posedness of martingale problem; Peano counter-example (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.04.012

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