%0 Journal Article
%T Asymptotics of Markov Kernels and the Tail Chain
%A Sidney I. Resnick
%A David Zeber
%J Mathematics
%D 2011
%I arXiv
%X 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.
%U http://arxiv.org/abs/1112.5747v1