A note on the Laplace--Varadhan integral lemma

Abstract

We propose a complement to the Laplace--Varadhan integral lemma arising in the large-deviations literature. We examine a situation in which the state space may depend on the rate of deviations. We use this framework to discuss large-deviations principles for an abstract class of discrete generation interacting particle systems as well as for pure jump and McKean--Vlasov diffusions.