Extreme events of Markov chains

Ioannis Papastathopoulos, Kirstin Strokorb, Jonathan A. Tawn, Adam Butler

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)134-161
Number of pages29
JournalAdvances in Applied Probability
Volume49
Issue number1
DOIs
Publication statusPublished - 17 Mar 2017

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