Max-analogues of N-infinite Divisibility and N-stability

摘要

Here we discuss the max-analogues of random infinite divisibility and random stability developed by Gnedenko and Korolev [5]. We give a necessary and sufficient condition for the weak convergence to a random max-infinitely divisible law from that to a max-infinitely divisible law. Introducing random max-stable laws we show that they are indeed invariant under random maximum. We then discuss their domain of max-attraction.