Large deviations built on max-stability

On large deviations mixing sequences

There is an extensive literature on the large deviation principle under various dependence structures. However, in comparison to other limit theorems, few papers deal with strong mixing dependence conditions. In this note we prove the large deviation principle for 4-mixing stationary random sequences with fast enough convergence rate and for $-mixing stationary random sequences. Our d-mixing re...

Large Deviations

Large Deviations

This paper is based on Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations. 1. Large deviations for sums. The role of " large deviations " is best understood through an example. Suppose that X random variables, for instance, normally distributed with mean zero and variance 1. Then, E e θ(X 1 +···+X n) = E[e θX ...

Large Deviations for Large Capacity

In this paper, we study large deviations of large capacity loss networks with xed routing. We use two-level modelling for the loss networks: the call level and the cell level. At the call level, a call request is accepted if it succeeds an admission test. The test is based on a polyhedral set of the number of calls in progress when a new call arrives. After being accepted, a call then transmits...

Nonequilibrium Markov Processes Conditioned on Large Deviations