Multilevel Monte Carlo for stochastic differential equations with additive fractional noise

被引：23

作者：

Kloeden, Peter E. ^{[1
]}

Neuenkirch, Andreas ^{[2
]}

Pavani, Raffaella ^{[3
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

[2] Tech Univ Dortmund, Fak Math, D-44227 Dortmund, Germany

[3] Politecn Milan, Dipartimento Matemat, I-20155 Milan, Italy

来源：

ANNALS OF OPERATIONS RESEARCH | 2011年 / 189卷 / 01期

关键词：

SDEs with additive noise; Fractional Brownian motion; Multilevel Monte Carlo; Euler scheme; Malliavin calculus; DRIVEN; APPROXIMATION; CONVERGENCE; SIMULATION; SDES;

D O I：

10.1007/s10479-009-0663-8

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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).

引用

页码：255 / 276

页数：22

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