Sanov's Theorem for White Noise Distributions and Application to the Gibbs Conditioning Principle

摘要

We consider a positive distribution Phi such that Phi defines a probability measure mu = mu Phi on the dual of some real nuclear Frechet space. A large deviation principle is proved for the family {mu(n), n >= 1} where mu(n) denotes the image measure of the product measure mu(n)(Phi) under the empirical distribution function L-n. Here the rate function I is defined on the space F-theta'(N')(+) and agrees with the relative entropy function (H) over tilde (Psi/Phi). As an application, we cite the Gibbs conditioning principle which describes the limiting behaviour as n tends to infinity of the law of k tagged particles Y-1,...,Y-k under the constraint that L-n(Y) belongs to some subset A(0).