A confidence interval for Monte Carlo methods with an application to simulation of obliquely reflecting Brownian motion
type: Item
instance of: scholarly article
title: A confidence interval for Monte Carlo methods with an application to simulation of obliquely reflecting Brownian motion
zbMATH Open document ID: 0645.62027
DOI: 10.1016/0304-4149(88)90038-5
author: Antonella Calzolari
author: C. Costantini
author: Federico Marchetti
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with the estimate of errors introduced by finite sampling in Monte Carlo evaluation of functionals of stochastic processes. To this end we introduce a metric d over the space of probability measures which induces a topology finer than the weak topology. For any two measures \(\mu\), \(\nu\), this metric allows to bound \(| <\mu,f>-<\nu,f>|\), uniformly over a large class of \(C^ 1\)- functions f, by a quantity which can be computed by a finite number of calculations. In the case \(\nu =\mu_ n\), the empirical distribution of order n of \(\mu\), we can compute the minimum sample size that will ensure that this quantity will be smaller than any given \(\epsilon\), at any chosen confidence level. As an application we control the rate of convergence of an approximating scheme for obliquely reflecting Brownian motion on a half-plane by a Monte Carlo evaluation of two significant functionals on the path space.
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J50
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4052787
zbMATH Keywords: Vapnis-Chervonenkis estimates
zbMATH Keywords: weak convergence
zbMATH Keywords: estimate of errors
zbMATH Keywords: finite sampling
zbMATH Keywords: Monte Carlo evaluation of functionals of stochastic processes
zbMATH Keywords: empirical distribution
zbMATH Keywords: minimum sample size
zbMATH Keywords: rate of convergence
zbMATH Keywords: approximating scheme
zbMATH Keywords: reflecting Brownian motion
MaRDI profile type: Publication
full work available at URL: 0304-4149(88)90038-5
OpenAlex ID: W2052591547
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description: scientific article; zbMATH DE number 4052787