Preliminary list of abstracts

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Multi-level algorithms for infinite-dimensional integration
Keywords: integration on the sequence space; variable subspace sampling; QMC-rules
Mon, 11:35--12:00
  • Ritter, Klaus (Department of Mathematics, TU Kaiserslautern, Germany)

Stochastic multi-level algorithms have turned out to be a powerful tool for variance reduction in different settings. In this talk, emphasis will be given to the study of integration on (subsets of) the product space ${\mathbb R}^{\mathbb N}$, which is motivated by, e.g., series expansions of stochastic processes. We show how to combine the multi-level technique and variable subspace sampling with (randomized) Quasi-Monte-Carlo-rules for integration on high-dimensional spaces ${\mathbb R}^d$. The analysis is based on known tractability results, which provide uniform error and cost bounds for high-dimensional integration as $d \to \infty$. Our analysis is complemented by numerical experiments for path-dependent options.

Joint work with Fred Hickernell (IIT, Chicago), Sebastian Mayer (TU Darmstadt), Thomas Müller-Gronbach (Universität Passau), and Ben Niu (IIT, Chicago). Supported by the DFG within Priority Program 1324.