Solutions to rough differential equations

  • Peter K. Friz
  • Martin Hairer
Part of the Universitext book series (UTX)


We show how to solve differential equations driven by rough paths by a simple Picard iteration argument. This yields a pathwise solution theory mimicking the standard solution theory for ordinary differential equations. We start with the simple case of differential equations driven by a signal that is sufficiently regular for Young’s theory of integration to apply and then proceed to the case of more general rough signals.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Peter K. Friz
    • 1
    • 3
  • Martin Hairer
    • 2
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Department of MathematicsImperial College LondonLondonUK
  3. 3.Weierstraß-Institut für Angewandte Analysis und StochastikBerlinGermany

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