Multilevel Monte Carlo Approximation of Functions

DOI10.1137/17M1135566zbMath1490.65023OpenAlexW2893228383WikidataQ129183972 ScholiaQ129183972MaRDI QIDQ4611517

Fabio Nobile, Sebastian Krumscheid

Publication date: 21 January 2019

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1135566

zbMATH Keywords

momentscharacteristic functiondistribution functionquantilesmultilevel Monte Carloconditional value-at-riskparametric expectation

Mathematics Subject Classification ID

Statistical methods; risk measures (91G70) Probabilistic models, generic numerical methods in probability and statistics (65C20) Monte Carlo methods (65C05) Characteristic functions; other transforms (60E10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Algorithms for approximation of functions (65D15) Complexity and performance of numerical algorithms (65Y20)

Related Items (5)

Estimation of distributions via multilevel Monte Carlo with stratified sampling ⋮ Quantifying uncertainties in contact mechanics of rough surfaces using the Multilevel Monte Carlo method ⋮ Budget-limited distribution learning in multifidelity problems ⋮ Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method ⋮ On Multilevel Best Linear Unbiased Estimators

Cites Work

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• On the Laplace transform of the lognormal distribution
• Multi-level stochastic approximation algorithms
• Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients
• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• Estimation of arbitrary order central statistical moments by the multilevel Monte Carlo method
• On irregular functionals of SDEs and the Euler scheme
• Optimal error bounds for cubic spline interpolation
• Monte Carlo complexity of global solution of integral equations
• Markov and Bernstein type inequalities for polynomials
• General multilevel adaptations for stochastic approximation algorithms of Robbins-Monro and Polyak-Ruppert type
• High dimensional polynomial interpolation on sparse grids
• Quantifying uncertain system outputs via the multilevel Monte Carlo method. I: Central moment estimation
• Convergence analysis of multilevel Monte Carlo variance estimators and application for random obstacle problems
• Approximation of probability density functions by the multilevel Monte Carlo maximum entropy method
• Stochastic simulation: Algorithms and analysis
• Multilevel Monte Carlo Methods
• Uncertainty Quantification for Approximate $p$-Quantiles for Physical Models with Stochastic Inputs
• Multilevel Monte Carlo Approximation of Distribution Functions and Densities
• Multilevel Monte Carlo Path Simulation
• Multilevel Estimation of Rare Events
• Mappings of Gaussian Cylindrical Measures in Banach Spaces
• Asymptotic Statistics
• Multilevel Nested Simulation for Efficient Risk Estimation
• The Mathematical Theory of Finite Element Methods
• Estimation of Non-Unique Quantiles
• The lognormal characteristic function
• A practical guide to splines.

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