On the Cramér transform, large deviations in boundary value problems, and the conditional invariance principle
type: Item
instance of: scholarly article
title: On the Cramér transform, large deviations in boundary value problems, and the conditional invariance principle
zbMATH Open document ID: 0915.60043
DOI: 10.1007/BF02109831
published in: Siberian Mathematical Journal
publication date: 1999-07-04T00:00:00Z
review text: Let \(S(n)\) denote the sum of \(n\) independent, identically distributed random variables \((\xi(i), i=1,2, \dots)\) in \(\mathbb{R}^d\) and let \(\Delta(x)\) be a \(d\)-dimensional cube around \(x\). The author gives a probabilistic interpretation of the Cramér transform in terms of the limit \(\lim_{n\to\infty}P[\xi(k(n))\in B\mid S(n)\in\Delta(x(n))]\). He then applies this result to the study of asymptotics of \(P[S(n)\in\Delta(x)\), \(S(1)\notin W_1,\dots,S(n-1)\notin W_{n-1}]\) and other problems with boundaries. In addition, he generalises the conditional invariance principle.
reviewed by: O.Brockhaus
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 923516
zbMATH Keywords: Cramér transform
zbMATH Keywords: large deviations
zbMATH Keywords: conditional invariance principle
author: A. A. Borovkov
MaRDI profile type: Publication
cites work: Sanov property, generalized I-projection and a conditional limit theorem
cites work: Q3840949
cites work: CONVERGENCE OF MEASURES AND RANDOM PROCESSES
cites work: Q3938260
cites work: Q4516320
cites work: Q5571407
cites work: On the Rate of Convergence in the “Conditional” Invariance Principle
cites work: Boundary-Value Problems for Random Walks and Large Deviations in Function Spaces
cites work: Q3866823
full work available at URL: https://doi.org/10.1007/bf02109831
OpenAlex ID: W2328149345
description: scientific article; zbMATH DE number 923516