BFS 2002 

Contributed Talk 
Laurent (Anh) Nguyen, Benjamin Jourdain
We give a necessary and sufficient condition for the a.s. existence of a positive integer N such that for all n larger than N, there is a probability measure which minimizes the relative entropy with respect to the empirical distribution associated with the n first variables of a sequence of i.i.d. random variables, under a "moment" constraint.
Under this condition, we prove that a.s. this probability measure converges weakly to the generalized solution of the constrained minimization of the relative entropy with respect to the common law of the i.i.d. random variables.