Seminar Product Disintegrations of Markov Chains: EVT and an Application to Climate Data

Title
Product Disintegrations of Markov Chains: EVT and an Application to Climate Data
(joint work with Sabrina Mulinacci and Rodrigo Fonseca)

Abstract
For a given sequence of random variables, Borsato et al. (2024, Statistics & Probability Letters, Volume 208) introduce the concept of a product disintegration, which is a latent sequence of random probability measures upon which conditioning makes the original sequence independent, and such that a fixed point condition holds for the conditioning operator. Drawing from these authors, we show constructively that any discrete-time Markov chain on a countable state space admits, under mild conditions, a non-trivial product disintegration which is also a Markov chain. In an EVT framework, we derive the “quenched” limit for the conditional distribution of the maximum of such chains, and obtain bounds for the “annealed” limit. Finally, we present a brief application to precipitation data.

Local Organizer: Umberto Cherubini