Variable Subspace Sampling and Multi-level Algorithms

Thomas Müller-Gronbach () and Klaus Ritter
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Thomas Müller-Gronbach: Universität Passau, Fakultät für Informatik und Mathematik

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 131-156 from Springer

Abstract: Abstract We survey recent results on numerical integration with respect to measures μ on infinite-dimensional spaces, e.g., Gaussian measures on function spaces or distributions of diffusion processes on the path space. Emphasis is given to the class of multi-level Monte Carlo algorithms and, more generally, to variable subspace sampling and the associated cost model. In particular we investigate integration of Lipschitz functionals. Here we establish a close relation between quadrature by means of randomized algorithms and Kolmogorov widths and quantization numbers of μ. Suitable multi-level algorithms turn out to be almost optimal in the Gaussian case and in the diffusion case.

Keywords: Minimal Error; Fractional Brownian Motion; Random Element; Gaussian Measure; Monte Carlo Algorithm (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_8

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DOI: 10.1007/978-3-642-04107-5_8

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