REGULARIZATION BY NOISE FOR ROUGH DIFFERENTIAL EQUATIONS DRIVEN BY GAUSSIAN ROUGH PATHS

• 成果类型: Article
• 署名作者: Catellier, Remi; Duboscq, Romain
• 署名单位: Inria; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1701
• 发表日期: 2025
• 页码: 79-139
• 关键词: multiplicative noise; Integrability

摘要

We consider the rough differential equation with drift driven by a Gaussian geometric rough path. Under natural conditions on the rough path, namely nondeterminism, and uniform ellipticity conditions on the diffusion coefficient, we prove path-by-path well-posedness of the equation for poorly regular drifts. In the case of the fractional Brownian motion B(H )for H > (1) (4), we prove that the drift may be taken to be kappa > 0 H & ouml;lder continuous and bounded for kappa > (3)(2) - (1) (2H) . A flow transform of the equation and Malliavin 1 calculus for Gaussian rough paths are used to achieve such a result.