Multilevel Monte Carlo for stochastic differential equations with additive fractional noise |
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| Authors: | Peter E Kloeden Andreas Neuenkirch Raffaella Pavani |
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| Institution: | 1.Institut für Mathematik,Johann Wolfgang Goethe Universit?t,Frankfurt am Main,Germany;2.Fakult?t für Mathematik,Technische Universit?t Dortmund,Dortmund,Germany;3.Dipartimento di Matematica,Politecnico di Milano,Milano,Italy |
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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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