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arXiv · 2107.04325

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

L. Marino·S. Menozzi
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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.

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L. Marino, S. Menozzi. 2021-07-09. Weak well-posedness for degenerate SDEs driven by L\'evy processes. https://arxiv.org/abs/2107.04325

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