Asymptotics of Markov Kernels and the Tail Chain

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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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA585087

Entities

People

  • David Zeber
  • Sidney Resnick

Organizations

  • Cornell University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Continuity
  • Convergence
  • Distribution Functions
  • Integrals
  • Markov Chains
  • Notation
  • Probability
  • Probability Distributions
  • Random Variables
  • Random Walk
  • Sequences
  • Stationary
  • Stationary Processes
  • Stochastic Processes
  • Theorems
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.