IDENTIFYING A LARGE DEVIATION RATE-FUNCTION

Assume a sequence of probabilities {P(n)} has a large deviation rate function I. It is proved that I takes a form analogous to a convex conjugate. If I is also assumed convex, then I is a convex conjugate of an explicitly defined function psi. The results are applied to the empirical law of a Markov chain yielding universal bounds on I. Examples are given of Markov chains in which the empirical law has a large deviation rate strictly between the given bounds.