where ess inf denotes the
essential infimum. Heuristically, this may be read as saying that for large θ,
Application
The Laplace principle can be applied to the family of
probability measuresPθ given by
to give an asymptotic expression for the probability of some event A as θ becomes large. For example, if X is a standard
normally distributedrandom variable on R, then
Dembo, Amir; Zeitouni, Ofer (1998). Large deviations techniques and applications. Applications of Mathematics (New York) 38 (Second ed.). New York: Springer-Verlag. pp. xvi+396.
ISBN0-387-98406-2.
MR1619036