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

Paul-Eric Chaudru de Raynal; Stephane Menozzi

doi:10.1090/tran/7947

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arXiv · 1710.03620

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

Paul-Eric Chaudru de Raynal·Stephane Menozzi

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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 H{\"o}rmander 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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Paul-Eric Chaudru de Raynal, Stephane Menozzi. 2017-10-10. Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result. https://doi.org/10.1090/tran%2F7947

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