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

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  • Koch, Erwan
  • Robert, Christian Y.

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).

Suggested Citation

  • Koch, Erwan & Robert, Christian Y., 2019. "Geometric ergodicity for some space–time max-stable Markov chains," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 43-49.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:43-49
    DOI: 10.1016/j.spl.2018.06.014
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    1. R. Huser & A. C. Davison, 2014. "Space–time modelling of extreme events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 439-461, March.
    2. K. V. Mardia, 1999. "Directional statistics and shape analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 949-957.
    3. Miasojedow, Błażej, 2014. "Hoeffding’s inequalities for geometrically ergodic Markov chains on general state space," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 115-120.
    4. Padoan, S. A. & Ribatet, M. & Sisson, S. A., 2010. "Likelihood-Based Inference for Max-Stable Processes," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 263-277.
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