Clustering of rare events

Monday, October 28, 2024, 10:30 -- 11:00

This talk is on understanding how the rare events of deviation of sample mean from population mean cluster for data coming from a stationary process whose marginal distribution has all exponential moments finite. Conditional on the event that the average of the first n observations exceeds the population mean by a prefixed threshold, we study the asymptotic distribution of the length of time for which this deviation persists, as n goes to infinity. It turns out that the answer depends on the memory of the stationary process. In the short memory regime, the asymptotic conditional distribution of the persistence time is a law on the set of natural numbers, whereas in the long memory regime, the persistence time goes almost surely to infinity. In the latter regime, the asymptotic conditional law under an appropriate scaling is studied.

This is a joint work with Gennady Samorodnitsky.