Large deviations in Banach spaces of continuous functions and their applications
type: Item
instance of: scholarly article
title: Large deviations in Banach spaces of continuous functions and their applications
zbMATH Open document ID: 0972.60005
author: E. I. Ostrovskij
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: This paper examines the large deviation principle for independent and identically distributed copies of (not necessarily smooth) random fields, \(\tau_i\). Working with the Dudley metric, the author establishes deviations for \(u\in(0,\varepsilon_n n^{1/6})\) for a sequence \(\varepsilon_n\) decreasing to 0 such that \(\varepsilon_n n^{1/6}\) increases to infinity. The main theorem states that as \(n\rightarrow\infty\) \[ \lim\frac{P[\sup_{t\in T}|\sum_1^n \tau_i(t)/ \sqrt{n}|>u]} {P[\sup_{t\in T}|G(t)|>u]} =1, \] for \(G\) a suitable Gaussian field. Only an outline of the proof is provided. The author indicates how this result can be used to handle the error in a Monte Carlo approach to numeric integration.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 65C05
zbMATH DE Number: 1557738
zbMATH Keywords: large deviation principle
zbMATH Keywords: Dudley metric
zbMATH Keywords: random fields
zbMATH Keywords: numeric integration
reviewed by: Andre R. Dabrowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1557738