A probability inequality for obtaining lower bounds in the large deviation principle
type: Item
instance of: scholarly article
title: A probability inequality for obtaining lower bounds in the large deviation principle
zbMATH Open document ID: 0878.60022
DOI: 10.1007/BF02104669
published in: Siberian Mathematical Journal
publication date: 1997-11-10T00:00:00Z
review text: The universal tool for obtaining the upper bounds in the large deviation principle is the Chebyshev inequality. The aim of the article is to obtain a probability inequality which might estimate the probabilities \({\mathbf P}(\xi\in A)\) from below in cases when the latter are small, and which could be used for proving lower bounds in the large deviation principle. Such an inequality is proved, and the lower bound is expressed in terms of the deviation function and probabilities \({\mathbf P}(\xi^\lambda\in A)\), where \(\xi^\lambda\) is a random variable conjugate to \(\xi\) (via Cramér transform).
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1023930
zbMATH Keywords: large deviation principle
zbMATH Keywords: Legendre transform
zbMATH Keywords: Cramér transform
author: Anatoli Mogulskii
reviewed by: Birutė Kryžienė
MaRDI profile type: Publication
cites work: Boundary-Value Problems for Random Walks and Large Deviations in Function Spaces
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full work available at URL: https://doi.org/10.1007/bf02104669
OpenAlex ID: W1974862553
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description: scientific article; zbMATH DE number 1023930