Extreme events of Markov chains

Papastathopoulos, I., Strokorb, K. ORCID: https://orcid.org/0000-0001-8748-3014, Tawn, J. A. and Butler, A. 2017. Extreme events of Markov chains. Advances in Applied Probability 49 (1) , pp. 134-161. 10.1017/apr.2016.82

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Abstract

The extremal behaviour of a Markov chain is typically characterised 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 normalisation scheme, and reveal features which existing methods reduce to a degenerate form associated with nonextreme states.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Applied Probability Trust
ISSN:	0001-8678
Date of First Compliant Deposit:	17 March 2017
Date of Acceptance:	6 April 2016
Last Modified:	18 Nov 2024 12:45
URI:	https://orca.cardiff.ac.uk/id/eprint/99162

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