Max-stable processes are very relevant for the modelling of spatial extremes. In this paper, we focus on some processes belonging to the class of space-time max-stable models introduced in Embrechts et al. (2016). The mentioned processes are Markov chains with state space 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 previously mentioned state space is not locally compact, making the classical methodology to be found, e.g., in Meyn and Tweedie (2009), inapplicable. Instead, we use the fact that the state space is Polish and apply results on Markov chains with Polish state spaces presented in Hairer (2010). 查看全文>>