JournalsrmiVol. 31, No. 3pp. 901–934

Flows driven by rough paths

  • Ismaël Bailleul

    Université de Rennes 1, France
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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.

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

DOI 10.4171/RMI/858