Revista Matemática Iberoamericana

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Volume 31, Issue 3, 2015, pp. 901–934
DOI: 10.4171/RMI/858

Published online: 2015-10-29

Flows driven by rough paths

Ismaël Bailleul[1]

(1) Université de Rennes 1, France

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.

Keywords: Rough differential equations, flows, approximate flows, mean field differential equation

Bailleul Ismaël: Flows driven by rough paths. Rev. Mat. Iberoamericana 31 (2015), 901-934. doi: 10.4171/RMI/858