Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result
arXiv:1710.03620 · doi:10.1090/tran/7947
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{ö}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.
Transactions of the American Mathematical Society, American Mathematical Society, 2020