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Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

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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.

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Correspondence to Peter E. Kloeden.

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Partially supported by the DFG project “Pathwise numerical analysis of stochastic evolution equations”.

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Kloeden, P.E., Neuenkirch, A. & Pavani, R. Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. Ann Oper Res 189, 255–276 (2011). https://doi.org/10.1007/s10479-009-0663-8

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  • DOI: https://doi.org/10.1007/s10479-009-0663-8

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