Variance reduction by means of deterministic computation: Collision estimate
type: Item
instance of: scholarly article
title: Variance reduction by means of deterministic computation: Collision estimate
zbMATH Open document ID: 0974.65117
DOI: 10.1016/S0378-3758(99)00078-6
author: Stefan Heinrich
published in: Journal of Statistical Planning and Inference
publication date: 2001-11-29T00:00:00Z
review text: The paper studies the collision estimate of Monte Carlo methods for the solution of integral equations. A new variant of a variance reduction technique is proposed and analyzed. The paper modifies the classical Monte Carlo algorithm, the absorption scheme, developed in a recent paper of the author [Monte Carlo Methods Appl. 1, No. 4, 251-277 (1995; Zbl 0843.65096)] and uses instead the collision scheme technique. After presenting the new technique for the collision scheme it is shown that the variance is dominated by the square of the proximity of the respective kernels and right-hand sides in some functions space norms. The results of the author [loc. cit.] can then be carried over to the collision scheme, such as the Galerkin method to construct a neighbouring equation and the estimation of proximity of kernels as well as right-hand sides from certain parameters of that method.
reviewed by: Hans-Peter Altenburg
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45A05
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1436937
zbMATH Keywords: Monte Carlo method
zbMATH Keywords: variance reduction
zbMATH Keywords: collision estimate
zbMATH Keywords: integral equations
zbMATH Keywords: absorption scheme
zbMATH Keywords: Galerkin method
zbMATH Keywords: proximity of kernels
MaRDI profile type: Publication
cites work: Q5636210
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full work available at URL: s0378-3758(99)00078-6
OpenAlex ID: W2041695852
description: scientific article; zbMATH DE number 1436937