Deterministic multi-level algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)

DOI10.1016/j.jco.2010.08.001zbMath1218.65005OpenAlexW2125886176MaRDI QIDQ544124

Klaus Ritter, Ben Niu, Thomas Müller-Gronbach, Fred J. Hickernell

Publication date: 14 June 2011

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2010.08.001

zbMATH Keywords

algorithmsBrownian motionMonte Carlo methodAsian optionreproducing kernel Hilbert spacemulti-level methodtractabilityworst case errorfinancial derivativefixed subspace samplinginfinite-dimensional quadraturelow discrepancy pointstensor product spacesvariable subspace sampling

Mathematics Subject Classification ID

Related Items (20)

QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND ⋮ Embeddings of weighted Hilbert spaces and applications to multivariate and infinite-dimensional integration ⋮ Some Results on the Complexity of Numerical Integration ⋮ Liberating the dimension for \(L_2\)-approximation ⋮ On tractability of linear tensor product problems for \(\infty \)-variate classes of functions ⋮ On weighted Hilbert spaces and integration of functions of infinitely many variables ⋮ Tractability of approximation of \(\infty\)-variate functions with bounded mixed partial derivatives ⋮ Tractability of infinite-dimensional integration in the worst case and randomized settings ⋮ Efficient algorithms for multivariate and \(\infty\)-variate integration with exponential weight ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ Average case tractability of approximating ∞-variate functions ⋮ Quasi-Monte Carlo and \(\varepsilon\)-truncation dimension in ANOVA spaces ⋮ The cost of deterministic, adaptive, automatic algorithms: cones, not balls ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition ⋮ Hyperbolic cross approximation in infinite dimensions ⋮ Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration ⋮ \( \varepsilon \)-superposition and truncation dimensions in average and probabilistic settings for \(\infty \)-variate linear problems ⋮ Infinite-dimensional integration on weighted Hilbert spaces ⋮ Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients

Cites Work

• Liberating the dimension
• Infinite-dimensional quadrature and approximation of distributions
• Tractability of multivariate problems. Volume I: Linear information
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• Multi-level Monte Carlo algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
• Monte Carlo complexity of global solution of integral equations
• The existence of good extensible rank-1 lattices
• Infinite-dimensional integration on weighted Hilbert spaces
• The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
• Multilevel Monte Carlo Path Simulation
• Strong Tractability of Quasi‐Monte Carlo Quadrature Using Nets for Certain Banach Spaces
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