arXiv subjects

L. Marino

Publications and source records attributed to L. Marino.

2 recordsLinked to original sources

arXiv2023

Weak well-posedness for degenerate SDEs driven by Lévy processes

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 continuous and satisfy a weak Hörmander-like condition. In particular, we assume some non-degeneracy with respect to the components which transmit the noise. Moreover, we characterize, for some specific dynamics, through suitable counterexamples , the almost sharp regularity exponents that ensure the weak well-posedness for the associated SDE. As a by-product of our approach, we also derive some Krylov-type estimates for the density of the weak solutions of the considered SDE.

math.AP↗

arXiv2021

Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators

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 $\in$ R N , N $\ge$ 1, which satisfy the Kalman condition which is equivalent to the hypoellipticity condition. We prove the following stability result: the Schauder and Sobolev estimates associated with the corresponding parabolic Cauchy problem remain valid, with the same constant, for the parabolic Cauchy problem associated with a second order perturbation of L, namely for L + Tr(S(t)D 2) where S(t) is a non-negative N x N matrix depending continuously on t $\ge$ 0. Our approach relies on the perturbative technique based on the Poisson process introduced in [15].

math.AP↗