Stochastic differential equations

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


We identify the solution to a rough differential equation driven by the Itˆo or Stratonovich lift of Brownian motion with the solution to the corresponding stochastic differential equation. In combination with continuity of the Itˆo–Lyons maps, a quick proof of the Wong–Zakai theorem is given. Applications to Stroock–Varadhan support theory and Freidlin–Wentzell large deviations are briefly discussed.


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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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