  Max-stable processes are central models for spatial extremes. In this paper,
we focus on some space-time max-stable models introduced in Embrechts et al.
(2016). The processes considered induce discrete-time Markov chains taking
values in the space of continuous functions from the unit sphere of
$\mathbb{R}^3$ to $(0, \infty)$. We show that these Markov chains are
geometrically ergodic. An interesting feature lies in the fact that the state
space is not locally compact, making the classical methodology inapplicable.
Instead, we use the fact that the state space is Polish and apply results
presented in Hairer (2010).
