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Weak regularization by degenerate Lévy noise and its applications
Lorenzo Marino
After a general introduction about the regularization by noise phenomenon in the degenerate setting, the first part of this PhD thesis focuses at establishing the Schauder estimate…
Dimensional Universality of Schauder Estimates Constants for Fourth Order Heat-Type Equations
Nicolò Cangiotti, Lorenzo Marino
A new method to compute Schauder Estimates for multidimensional fourth order heat-type equations is proposed. In particular, we show how knowing Schauder or Sobolev estimates for t…
Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators
L. Marino, S. Menozzi, E. Priola
We consider a possibly degenerate Kolmogorov-Ornstein-Uhlenbeck operator of the form L = Tr(BD 2) + Az, D , where A, B are N x N matrices, z R N , N 1, which satisfy th…
Weak well-posedness for degenerate SDEs driven by Lévy processes
L. Marino, S. Menozzi
In this article, we study the effects of the propagation of a non-degenerate Lévy noise through a chain of deterministic differential equations whose coefficients are Hölder contin…