ASYMPTOTICS OF MARKOV KERNELS AND THE TAIL CHAIN

作者：Resnick Sidney I^*; Zeber David

来源：Advances in Applied Probability, 2013, 45(1): 186-213.

DOI：10.1239/aap/1363354108

• Extreme values
• multivariate regular variation
• Markov chain
• transition kernel
• tail chain
• heavy tail

An asymptotic model for the 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 nonextreme 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.

• 出版日期2013-3