Results 11 to 20 of about 545,959 (267)
Adaptive Multilevel Monte Carlo for Probabilities [PDF]
SIAM Journal on Numerical Analysis, 2021 We consider the numerical approximation of $\mathbb{P}[G\in \Omega]$ where the $d$-dimensional random variable $G$ cannot be sampled directly, but there is a hierarchy of increasingly accurate approximations $\{G_\ell\}_{\ell\in\mathbb{N}}$ which can be ...
A. Haji-Ali, J. Spence, A. Teckentrup
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Deflated Multigrid Multilevel Monte Carlo [PDF]
Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022), 2022 In lattice QCD, the trace of the inverse of the discretized Dirac operator appears in the disconnected fermion loop contribution to an observable. As simulation methods get more and more precise, these contributions become increasingly important.
A. Frommer, Gustavo Ramirez-Hidalgo
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A Continuation Multilevel Monte Carlo algorithm [PDF]
BIT Numerical Mathematics, 2014 We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error ...
Collier, Nathan +4 more
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Multilevel Monte Carlo methods [PDF]
Acta Numerica, 2013 Monte Carlo methods are a very general and useful approach for the estimation of expectations arising from stochastic simulation. However, they can be computationally expensive, particularly when the cost of generating individual stochastic samples is ...
M. Giles
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Adaptive Multilevel Splitting for Monte Carlo particle transport [PDF]
EPJ Web of Conferences, 2017 In the Monte Carlo simulation of particle transport, and especially for shielding applications, variance reduction techniques are widely used to help simulate realisations of rare events and reduce the relative errors on the estimated scores for a given ...
Louvin Henri +4 more
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A Multilevel Monte Carlo Estimator for Matrix Multiplication [PDF]
SIAM Journal on Scientific Computing, 2020 Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data.
Polydorides, Nick, Wu, Yue
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Multilevel Monte Carlo Path Simulation [PDF]
Operations Research, 2008 We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and a Euler discretisation, the computational cost to achieve an accuracy of O(ϵ) is reduced from O(ϵ−3) to O(ϵ−2 (
M. Giles
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Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems [PDF]
Mathematics of Computation, 2016 In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in
Kuo, Frances Y. +4 more
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From rough path estimates to multilevel Monte Carlo [PDF]
SIAM Journal on Numerical Analysis, 2016 New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations ...
Bayer, Christian +3 more
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Multilevel blocking Monte Carlo simulations for quantum dots [PDF]
International Journal of Modern Physics B, 1999 This article provides an introduction to the ideas behind the multilevel blocking (MLB) approach to the fermion sign problem in path-integral Monte Carlo simulations, and also gives a detailed discussion of MLB results for quantum dots.
Egger, R., Mak, C. H.
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