$Multilevel Monte Carlo for stochastic differential equations with additive fractional noise$

Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

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Article ID:	iaor20119387
Volume:	189
Issue:	1
Start Page Number:	255
End Page Number:	276
Publication Date:	Sep 2011
Journal:	Annals of Operations Research
Authors:	Kloeden E, Neuenkirch Andreas, Pavani Raffaella

Abstract:

We adopt the multilevel Monte Carlo method introduced by M. Giles (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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