Tilted large deviation principle
In mathematics — specifically, in large deviations theory — the tilted large deviation principle is a result that allows one to generate a new large deviation principle from an old one by "tilting", i.e. integration against an exponential functional. It can be seen as an alternative formulation of Varadhan's lemma.Let X be a Polish space, and let ε>0 be a family of probability measures on X that satisfies the large deviation principle with rate function I : X → . Let F : X → R be a continuous function that is bounded from above. For each Borel set S ⊆ X, let
and define a new family of probability measures ε>0 on X by
Then ε>0 satisfies the large deviation principle on X with rate function IF : X → given by
