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Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. (English) Zbl 1235.60064
Summary: We adopt the multilevel Monte Carlo method introduced by M. B. Giles [Oper. Res. 56, No. 3, 607–617 (2008; Zbl 1167.65316)] 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 \(\varepsilon \) with a computational effort of order \(\varepsilon^{-2}\).

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
Software:
SimEstFBM
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