Large Deviations Theory

Mathematical theory that characterizes the exponential decay rates of probabilities of rare events for a family or sequence of stochastic processes or random variables, typically by establishing a Large Deviations Principle (LDP) that provides asymptotic upper and lower bounds of the form P(X_n ∈ A) ≍ exp(-n I(A)) where I is a rate function describing the dominant exponential rate.