JournalsrmiVol. 31, No. 3pp. 901–934

Flows driven by rough paths

  • Ismaël Bailleul

    Université de Rennes 1, France
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Abstract

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.

Cite this article

Ismaël Bailleul, Flows driven by rough paths. Rev. Mat. Iberoam. 31 (2015), no. 3, pp. 901–934

DOI 10.4171/RMI/858