WIAS Preprint No. 1787, (2013)

From rough path estimates to multilevel Monte Carlo


  • Bayer, Christian
    ORCID: 0000-0002-9116-0039
  • Friz, Peter
    ORCID: 0000-0003-2571-8388
  • Riedel, Sebastian
  • Schoenmakers, John G. M.
    ORCID: 0000-0002-4389-8266

2010 Mathematics Subject Classification

  • 60H35 65C05 65C30


  • Rough paths, Fractional Brownian motion, Euler scheme, Multilevel Monte Carlo




Discrete approximations to solutions of stochastic differential equations are well-known to converge with strong rate 1/2. Such rates have played a key-role in Giles' multilevel Monte Carlo method [Giles, Oper. Res. 2008] which gives a substantial reduction of the computational effort necessary for the evaluation of diffusion functionals. In the present article similar results are established for large classes of rough differential equations driven by Gaussian processes (including fractional Brownian motion with H>1/4 as special case).

Appeared in

  • SIAM J. Numer. Anal., 54 (2016) pp. 1449--1483.

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