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

共 50 条

[31] On quasi-Monte Carlo simulation of stochastic differential equations
Hofmann, N
Mathe, P
MATHEMATICS OF COMPUTATION, 1997, 66 (218) : 573 - 589
[32] Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations
Oraby, T.
Suazo, E.
Arrubla, H.
CHAOS SOLITONS & FRACTALS, 2023, 166
[33] Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations
Oraby, T.
Suazo, E.
Arrubla, H.
CHAOS SOLITONS & FRACTALS, 2023, 166
[34] STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY AN ADDITIVE FRACTIONAL BROWNIAN SHEET
El Barrimi, Oussama
Ouknine, Youssef
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 56 (02) : 479 - 489
[35] A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise
Neuenkirch A.
Tindel S.
Statistical Inference for Stochastic Processes, 2014, 17 (1) : 99 - 120
[36] Weak exponential schemes for stochastic differential equations with additive noise
Mora, CM
IMA JOURNAL OF NUMERICAL ANALYSIS, 2005, 25 (03) : 486 - 506
[37] Spectral Element Methods for Stochastic Differential Equations with Additive Noise
Zhang, Chao
Gu, Dongya
Tao, Dongya
JOURNAL OF MATHEMATICAL STUDY, 2018, 51 (01): : 76 - 88
[38] Stochastic Fractional Hamiltonian Monte Carlo
Ye, Nanyang
Zhu, Zhanxing
PROCEEDINGS OF THE TWENTY-SEVENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, 2018, : 3019 - 3025
[39] THE NUMERICAL STABILITY OF STOCHASTIC ORDINARY DIFFERENTIAL EQUATIONS WITH ADDITIVE NOISE
Buckwar, E.
Riedler, M. G.
Kloeden, P. E.
STOCHASTICS AND DYNAMICS, 2011, 11 (2-3) : 265 - 281
[40] An averaging principle for fractional stochastic differential equations with Levy noise
Xu, Wenjing
Duan, Jinqiao
Xu, Wei
CHAOS, 2020, 30 (08)

← 1 2 3 4 5 →