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Extreme events of Markov Chains

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>03/2017
<mark>Journal</mark>Advances in Applied Probability
Issue number1
Number of pages18
Pages (from-to)134-161
Publication StatusPublished
Early online date17/03/17
<mark>Original language</mark>English


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.