Optimal designs for weighted approximation and integration of stochastic processes on [0, ∞)

Leszek Plaskota, Klaus Ritter, Grzegorz W. Wasilkowski

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We study minimal errors and optimal designs for weighted L2-approximation and weighted integration of Gaussian stochastic processes X defined on the half-line [0, ∞). Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration. The upper bounds are proven constructively for approximation and non-constructively for integration. For integration of the r-fold integrated Brownian motion, the upper bound is proven constructively and we have a matching lower bound.

Original languageEnglish
Pages (from-to)108-131
Number of pages24
JournalJournal of Complexity
Volume20
Issue number1
DOIs
StatePublished - Feb 2004

Bibliographical note

Funding Information:
The first author was supported, in part, by the State Committee for Sc ientific Research of Poland (KBN) under Grant 5 P03A 007 21. The third author was partially supported by the National Sc ienc e Foundation under Grant CCR-0095709.

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics (all)
  • Control and Optimization
  • Applied Mathematics

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