Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes

2024/10/17 by Giacomo Lucertini, Lucertini, Giacomo, Stéphane Menozzi +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H10 #60H30 #60H50 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2410.13432

openalex publication_date 2024/10/17 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28

Abstract

We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric α-stable process under Hölder regularity conditions for the drift term. We partially recover the thresholds for the Hölder regularity that are optimal for weak uniqueness. In general dimension, we only consider α= 2 and need an additional integrability assumption for the gradient of the drift: this condition is satisfied by Peano-type functions. In the one-dimensional case we do not need any additional assumption. In the multi-dimensional case, the proof is based on a first-order Zvonkin transform/PDE, while for the one-dimensional case we use a second-order Zvonkin/PDE transform together with a Watanabe-Yamada technique.

Related

• Strong regularization by noise for kinetic SDEs
• Strong regularization by Brownian noise propagating through a weak Hörmander structure
• Well-posedness of some non-linear stable driven SDEs
• Weak regularization by degenerate Lévy noise and its applications
• Hölder regularity and gradient estimates Hölder regularity and gradient estimates for SDEs driven by cylindrical α-stable processes