Strong regularization by Brownian noise propagating through a weak Hormander structure

• 成果类型: Article
• 署名作者: De Raynal, Paul-Eric Chaudru; Honore, Igor; Menozzi, Stephane
• 署名单位: Nantes Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Saclay; HSE University (National Research University Higher School of Economics)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01150-z
• 发表日期: 2022
• 页码: 1-83
• 关键词: differential-equations; l-p; pathwise uniqueness; strong existence; sdes; Operators; density; driven; drift; pdes

摘要

We establish strong uniqueness for a class of degenerate SDEs of weak Hormander type under suitable Holder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit good smoothing properties of the underlying parabolic PDE with rough, here Holder, drift coefficients and source term. Such regularizing effects are established through a perturbation technique (forward parametrix approach) which also heavily relies on appropriate duality properties on Besov spaces. For the method employed, we exhibit some sharp thresholds on the Holder exponents for the strong uniqueness to hold.