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Accession Number ADA585087
Title Asymptotics of Markov Kernels and the Tail Chain.
Publication Date 2013
Media Count 27p
Personal Author D. Zeber S. I. Resnick
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.
Keywords Asymptotics
Extreme values
Heavy tails
Markov chains
Markov processes
Multivariate regular variations
Tail chains
Transition kernels

Source Agency Non Paid ADAS
NTIS Subject Category 72F - Statistical Analysis
41J - Tooling, Machinery, & Tools
Corporate Author Cornell Univ., Ithaca, NY.
Document Type Technical report
Title Note Technical rept.
NTIS Issue Number 1403
Contract Number W911NF-10-1-0289

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