Extreme events of Markov Chains

Papastathopoulos, Ioannis and Strokorb, Kirstin and Tawn, Jonathan Angus and Butler, Adam (2017) Extreme events of Markov Chains. Advances in Applied Probability, 49 (1). pp. 134-161. ISSN 0001-8678

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The extremal behaviour of a Markov chain is typically characterized by its tail chain. For asymptotically dependent Markov chains existing formulations fail to capture the full evolution of the extreme event when the chain moves out of the extreme tail region and for asymptotically independent chains recent results fail to cover well-known asymptotically independent processes such as Markov processes with a Gaussian copula between consecutive values. We use more sophisticated limiting mechanisms that cover a broader class of asymptotically independent processes than current methods, including an extension of the canonical Heffernan-Tawn normalization scheme, and reveal features which existing methods reduce to a degenerate form associated with non-extreme states.

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Journal Article
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Advances in Applied Probability
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05 Jan 2017 15:14
Last Modified:
18 Sep 2023 01:08