Flows driven by rough paths

• Ismaël Bailleul ^[1]
  1. [1] Université de Rennes
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 3, 2015, págs. 901-934
• Idioma: inglés
• DOI: 10.4171/RMI/858
• Texto completo no disponible (Saber más ...)
• Resumen

  • We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main existence and well-posedness results for rough differential equations, in the context of dynamics on a Banach space driven by a Hölder weak geometric rough path; the explosion question under linear growth conditions, Taylor expansion and Euler estimates are also dealt with. We illustrate our approach by proving an existence and well-posedness result for some mean field stochastic rough differential equation.