Stationary max-stable processes with the Markov property

TL;DR

This paper characterizes stationary max-stable processes with the Markov property, showing they are equivalent to max-autoregressive processes of order 1, up to time reversal, in both discrete and continuous time.

Contribution

It establishes a complete classification of stationary max-stable Markov processes as max-autoregressive of order 1, extending the understanding of their structure.

Findings

Max-stable Markov processes are equivalent to max-autoregressive processes of order 1.

The classification holds for both discrete and continuous time processes.

The results include a time reversal symmetry in the process class.

Abstract

We prove that the class of discrete time stationary max-stable process satisfying the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order $1$. A similar statement is also proved for continuous time processes.