ROUGH EVOLUTION EQUATIONS

• 成果类型: Article
• 署名作者: Gubinelli, Massimiliano; Tindel, Samy
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite de Lorraine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP437
• 发表日期: 2010
• 页码: 1-75
• 关键词: fractional brownian-motion; differential-equations; driven; INTEGRALS; paths

摘要

We generalize Lyons' rough paths theory in order to give a pathwise meaning to some nonlinear infinite-dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space-time Gaussian noise with singular space covariance and Brownian time dependence.