Conditional independence among max-stable laws

Ioannis Papastathopoulos, Kirstin Strokorb

Published 2015-06-12Version 1

Let $X$ be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint sub-vectors of $X$ given the remaining components implies their joint independence. We conclude that a broad class of tractable max-stable models cannot exhibit an interesting Markov structure.