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Introduction

Chapter
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Part of the Universitext book series (UTX)

Abstract

Consider the following situation. E is a Polish space and {µε: ε > 0} is a family of probability measures on E such that µε\( {\mu_{\varepsilon }} \Rightarrow {\delta_{{{x_o}}}} \) as ε ↓ 0 (i.e., µε converges weakly to the unit mass at xo). The study of large deviations is the study of how fast µε (Γ) → 0 for Γ ∈ \( \Gamma \in {\beta_E} \) such that xo \( {x_0} \notin \bar{\Gamma } \) Γ̄. In particular, we will be studying situations in which this convergence is exponentially fast and we will be seeking expressions for
$$ - \mathop{{\lim }}\limits_{{\varepsilon \downarrow 0}} \varepsilon \log {\mu_{\varepsilon }}(\Gamma ) $$
.

Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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