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A Strong Law of Large Numbers for Scrambled Net Integration

This article provides a strong law of large numbers for integration on digital nets randomized by a nested uniform scramble. The motivating problem is optimization over some variables of an integral over others, arising in Bayesian optimization. This strong law requires that the integrand have a finite moment of order $p$ for some $p>1$. Previously known results implied a strong law only for Riemann integrable functions. Previous general weak laws of large numbers for scrambled nets require a square integrable integrand. We generalize from $L^2$ to $L^p$ for $p>1$ via the Riesz--Thorin interpolation theorem.

Ketersediaan

Informasi Detail

Judul Seri

SIAM REVIEW; Vol.63 No.2 June 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 360 - 372

Bahasa

English

ISBN/ISSN

-

Klasifikasi

-

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SIMULATION-OPTIMIZATION
QUADRATURE
CUBATURE
QUASI--MONTE CARLO
RANDOMIZED QUASI--MONTE CARLO

Info Detail Spesifik

https://doi.org/10.1137/20M1320535

Pernyataan Tanggungjawab

Art B. Owen, Daniel Rudolf

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