Asymptotics of Markov Kernels and the Tail Chain

Details Asymptotics of Markov Kernels and the Tail Chain Asymptotics of Markov Kernels and the Tail Chain

2011-12-24

arxiv.org/abs/1112.5747v1

Mathematics

Probability

24 pages, submitted to Advances in Applied Probability

Scientific paper

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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