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

Leszek Plaskota; Klaus Ritter; Grzegorz W. Wasilkowski

doi:10.1016/j.jco.2003.10.002

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

Leszek Plaskota, Klaus Ritter, Grzegorz W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	108-131
Number of pages	24
Journal	Journal of Complexity
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/j.jco.2003.10.002
State	Published - 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
General Mathematics
Control and Optimization
Applied Mathematics

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10.1016/j.jco.2003.10.002

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

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.",

author = "Leszek Plaskota and Klaus Ritter and Wasilkowski, {Grzegorz W.}",

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.",

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AU - Plaskota, Leszek

AU - Ritter, Klaus

AU - Wasilkowski, Grzegorz W.

N1 - 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.

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N2 - 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.

AB - 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.

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JO - Journal of Complexity

JF - Journal of Complexity

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

Abstract

Bibliographical note

ASJC Scopus subject areas

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