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

Erwan Koch and Christian Y. Robert

Statistics & Probability Letters, 2019, vol. 145, issue C, 43-49

Abstract: 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 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).

Keywords: Geometric ergodicity; Markov chains with non locally compact state space; Space–time max-stable processes on a sphere; Spectral separability (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2018.06.014

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