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Annals of Operations Research

, Volume 189, Issue 1, pp 255–276 | Cite as

Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

  • Peter E. KloedenEmail author
  • Andreas Neuenkirch
  • Raffaella Pavani
Article

Abstract

We adopt the multilevel Monte Carlo method introduced by M. Giles (Multilevel Monte Carlo path simulation, Oper. Res. 56(3):607–617, 2008) to SDEs with additive fractional noise of Hurst parameter H>1/2. For the approximation of a Lipschitz functional of the terminal state of the SDE we construct a multilevel estimator based on the Euler scheme. This estimator achieves a prescribed root mean square error of order ε with a computational effort of order ε −2.

SDEs with additive noise Fractional Brownian motion Multilevel Monte Carlo Euler scheme Malliavin calculus 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Peter E. Kloeden
    • 1
    Email author
  • Andreas Neuenkirch
    • 2
  • Raffaella Pavani
    • 3
  1. 1.Institut für MathematikJohann Wolfgang Goethe UniversitätFrankfurt am MainGermany
  2. 2.Fakultät für MathematikTechnische Universität DortmundDortmundGermany
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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