A special edition of the YRM in which we welcome a speaker from outside the statistics department. Mnerh Alqahtani from the maths department will speak about:

The effect of rate function properties on exponential tilting

Large deviation theory is the theory behind quantifying the probability of rare and extreme events. These are of interest to physicists, actuaries and biologists, depending on the underlying system. If a large deviation principle (LDP) holds, then the probability of these tail events decays exponentially, but the dominating contribution can be estimated from the rate function. This talk presents a difficulty in probing these unlikely events in a stochastic differential equation, when the quantity of interest has a heavy-tailed distribution. In this case, the standard procedure, which is exponential tilting, fails. I offer a solution which is a non-linearly tilting, justified by the Gärtner-Ellis theorem, including the duality between the cumulant generating function (CGF) and the rate function.