Rough weak solutions for singular Lévy SDEs

• 成果类型: Article
• 署名作者: Kremp, Helena; Perkowski, Nicolas
• 署名单位: Technische Universitat Wien; Free University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01371-y
• 发表日期: 2025
• 页码: 483-537
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; regularization; uniqueness

摘要

We introduce a weak solution concept (called rough weak solutions) for singular SDEs with additive alpha-stable L & eacute;vy noise (including the Brownian noise case) and prove its well-posedness and equivalence to martingale solutions from Kremp and Perkowski (Bernoulli 28(3):1757-1783, 2022. https://doi.org/10.3150/21-BEJ1394) in Young and rough regularity regimes. In the rough regime this requires to construct certain rough integrals with the help of the stochastic sewing lemma, which we use to prove a generalized It & ocirc; formula for rough weak solutions. Furthermore, we show that in the Young case our solutions are equivalent to a simpler notion of weak solution, while in the rough case this simpler formulation leads to non-uniqueness in law.