An Introduction to (Stochastic) Calculus with Respect to Fractional Brownian Motion

  • Laure Coutin
Part of the Lecture Notes in Mathematics book series (LNM, volume 1899)

This survey presents three approaches to (stochastic) integration with respect to fractional Brownian motion. The first, a completely deterministic one, is the Young integral and its extension given by rough path theory; the second one is the extended Stratonovich integral introduced by Russo and Vallois; the third one is the divergence operator. For each type of integral, a change of variable formula or Ito formula is proved. Some existence and uniqueness results for differential equations driven by fractional Brownian motion are available except for the divergence integral. As soon as possible, these integrals are compared. Key words: Gaussian processes, Fractional Brownian motion, Rough path, Stochastic calculus of variations

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© Springer-VerlagBerlinHeidelberg 2007

Authors and Affiliations

  • Laure Coutin
    • 1
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse Cedex 4France

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