Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

作者：Kloeden Peter E^*; Neuenkirch Andreas; Pavani Raffaella

来源：Annals of Operations Research, 2011, 189(1): 255-276.

DOI：10.1007/s10479-009-0663-8

• SDEs with additive noise
• Fractional Brownian motion
• Multilevel Monte Carlo
• Euler scheme
• Malliavin calculus

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 epsilon with a computational effort of order epsilon (-2).

• 出版日期2011-9