The space of rough paths

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


We define the space of (H¨older continuous) rough paths, as well as the subspace of “geometric” rough paths which preserve the usual rules of calculus. The latter can be interpreted in a natural way as paths with values in a certain nilpotent Lie group. At the end of the chapter, we give a short discussion showing how these definitions should be generalised to treat paths of arbitrarily low regularity.


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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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