Geometric ergodicity for some space–time max-stable Markov chains

Publication date: Available online 20 July 2018Source: Statistics & Probability LettersAuthor(s): Erwan Koch, Christian Y. RobertAbstractMax-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 R3 to (0,∞). 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).

Source: Statistics and Probability Letters - July 20, 2018 Category: Statistics Source Type: research