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Cameron–Martin regularity and applications

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

Abstract

A continuous Gaussian process gives rise to a Gaussian measure on path-space. Thanks to variation regularity properties of Cameron–Martin paths, powerful tools from the analysis on Gaussian spaces become available. A general Fernique type theorem leads us to integrability properties of rough integrals with Gaussian integrator akin to those of classical stochastic integrals. We then discuss Malliavin calculus for differential equations driven by Gaussian rough paths. As application a version of H¨ormander’s theorem in this non-Markovian setting is established.

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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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