CONDITIONAL EXTREMES OF A MARKOV CHAIN
Adam Butler, Biomathematics & Statistics Scotland
Statistics Seminar, Edinburgh University, 25 November 2005

ABSTRACT
Catastrophic events often occur when two or more processes simultaneously 
become extreme - for example, floods in coastal towns often occur when tide 
and rivers levels are both unusually high, and components of a machine often 
fail when all of the components within the machine fail simultaneously. 
Quantification of the risks associated with such events requires that we 
understand dependence between random variables at extreme levels, and the 
development of models for multivariate extremes is currently an area of 
active research within both statistics and probability. 

In this talk we present a new model to describe dependence at extreme levels 
within a Markov chain, and discuss potential statistical applications of this 
model. The key features of our model are that it is able to allow for asymptotic 
independence as well as asymptotic dependence, and that it provides a parsimonious 
description of extremal dependence within a fairly broad class of Markov models.