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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2020

Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result

Résumé

We investigate the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like Hörmander structure (i.e. a non-degeneracy condition w.r.t. the components which transmit the noise). In particular we characterize, through suitable counterexamples , almost sharp regularity exponents that ensure that weak well posedness holds for the associated SDE. As a by-product of our approach, we also derive some density estimates of Krylov type for the weak solutions of the considered SDEs.
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Dates et versions

hal-01613679 , version 1 (09-10-2017)
hal-01613679 , version 2 (25-09-2020)
hal-01613679 , version 3 (31-10-2021)

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Paul-Eric Chaudru de Raynal, Stephane Menozzi. Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result. Transactions of the American Mathematical Society, 2020, ⟨10.1090/tran/7947⟩. ⟨hal-01613679v3⟩
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