Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion

  • Jan Gairing
  • Peter Imkeller
  • Radomyra Shevchenko
  • Ciprian TudorEmail author


We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the quadratic variations of the solution, defined via higher-order increments. Then we apply our results to construct and study estimators for the Hurst index.


Hurst index estimation Stochastic differential equation Fractional Brownian motion Quadratic variation Malliavin calculus Central limit theorem 

Mathematics Subject Classification (2010)

60G15 60H05 60G18 



R. Shevchenko acknowledges the financial support of the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823). C. Tudor acknowledges the partial support from the Labex CEMPI (ANR-11-LABX-0007-01) and MATHAMSUD project SARC (19-MATH-06).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jan Gairing
    • 1
  • Peter Imkeller
    • 2
  • Radomyra Shevchenko
    • 3
  • Ciprian Tudor
    • 4
    • 5
    Email author
  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMunichGermany
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Fakultät für MathematikTechnische Universität DortmundDortmundGermany
  4. 4.UMR 8524 Laboratoire Paul PainlevéCNRS, Université de Lille 1Villeneuve-d’AscqFrance
  5. 5.ISMMARomanian AcademyBucharestRomania

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