Operations on controlled rough paths

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


At first sight, the notation R Y dX introduced in Chapter 4 is ambiguous since the resulting controlled rough path depends in general on the choices of both the secondorder process X and the derivative process Y 0 . Fortunately, this “lack of completeness” in our notations is mitigated by the fact that in virtually all situations of interest, Y is constructed by using a small number of elementary operations described in this chapter. For all of these operations, it turns out to be intuitively rather clear how the corresponding derivative process is constructed.


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© 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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