A general non-convex large deviation result with applications to stochastic equations
type: Item
instance of: scholarly article
title: A general non-convex large deviation result with applications to stochastic equations
zbMATH Open document ID: 0993.60028
publication date: 2002-09-24T00:00:00Z
review text: The author proves an abstract large deviation result for a sequence of random elements \((Y_n)\) in a topological vector space \(E\) which generalizes classical results of Gärtner and Ellis to a non-convex situation. Instead of considering the logarithmic moment generating function \(\theta_n(\xi)= \log{\mathbf E}\exp\langle Y_n\xi\rangle\), \(\xi\in E^*\), he stipulates the existence of functions \(\Phi_n: E\times E^*\to {\mathbf R}\) satisfying the exponential martingale condition \({\mathbf E}(\exp\langle Y_n\xi\rangle-\Phi_n(Y_n \xi))= 1\) and the existence of the limit \(\lim_{n\to\infty} n^{-1}\Phi_n(x,n\xi)\) for every \(\xi\in E^*\). The results are applied to large deviation properties of the stochastic differential equations.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 1563073
zbMATH Keywords: large deviations
zbMATH Keywords: non-convex rate function
zbMATH Keywords: stochastic differential equation
author: Alejandro D. de Acosta
reviewed by: Michael Scheutzow
MaRDI profile type: Publication
DOI: 10.1007/S004400000095
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1563073