Eduardo Horta (UFRGS)

Title: Product Disintegrations of Markov Chains and EVT: Theory and Application to Climate Data

For a given sequence of random variables, Borsato et al. (2024,  Product disintegrations: A law of large numbers via conditional independence. Statistics & Probability Letters, Volume 208, 110056) introduce the concept of a product disintegration, which is a latent sequence of random probability measures such 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. Our construction is potentially relevant as it may establish a link between Markov chain theory and extreme value theory (joint work with Sabrina Mulinacci and Rodrigo Fonseca).