Document details for 'Extreme events of Markov chains'

Authors Papastathopoulos, I., Strokorb, K., Butler, A. and Tawn, J.A.
Publication details Journal of Applied Probability 49(1), 134-161. Cambridge University Press, Cambridge.
Publisher details Cambridge University Press, Cambridge
Keywords Asymptotic independence, conditional extremes, extreme value theory, Markov chains, hidden tail chain, tail chain
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.
Last updated 2018-04-12

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