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

Chaudru de Raynal, Paul-Éric; Menozzi, Stéphane

doi:10.1090/tran/7947

Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result
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by Paul-Éric Chaudru de Raynal and Stéphane Menozzi PDF

Trans. Amer. Math. Soc. 375 (2022), 1-45 Request permission

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 counter-examples, 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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