Asymptotics of Markov Kernels and the Tail Chain

2011/12/24 by Resnick, Sidney I., Zeber, David · 1 citation
#60G70 #60J05 (Primary) #62P05 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1112.5747

Abstract

An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and non-extreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regular variation property of the finite-dimensional distributions under assumptions on the marginal tails alone.

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• Markov chains, AR linear models, and regular variation

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