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

Abstract : 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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Contributor : Stephane Menozzi <>
Submitted on : Monday, October 9, 2017 - 11:28:18 PM
Last modification on : Friday, July 20, 2018 - 11:13:05 AM
Long-term archiving on : Wednesday, January 10, 2018 - 2:59:29 PM

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  • HAL Id : hal-01613679, version 1
  • ARXIV : 1710.03620

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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. 2017. ⟨hal-01613679⟩

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