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Brownian motion as a rough path

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

Abstract

In this chapter, we consider the most important example of a rough path, which is the one associated to Brownian motion. We discuss the difference, at the level of rough paths, between Ito and Stratonovich Brownian motion. We also provide a natural example of approximation to Brownian motion which converges to neither of them.

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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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