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Article Dans Une Revue Stochastic Processes and their Applications Année : 2023

Weak well-posedness for degenerate SDEs driven by Lévy processes

Résumé

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 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-ype estimates for the density of the weak solutions of the considered SDE.
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Dates et versions

hal-03281998 , version 1 (08-07-2021)

Identifiants

Citer

L Marino, S Menozzi. Weak well-posedness for degenerate SDEs driven by Lévy processes. Stochastic Processes and their Applications, 2023, 162, pp.106-170. ⟨10.1016/j.spa.2023.04.012⟩. ⟨hal-03281998⟩
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