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B0799
Title: Regularly varying Markov trees Authors:  Johan Segers - Universite catholique de Louvain (Belgium) [presenting]
Gildas Mazo - Universite Catholique de Louvain (Belgium)
Abstract: Extreme values of regularly varying Markov chains can be described in terms of the limiting conditional distribution of the normalized chain given that it is large at a particular time instant. The limit distributions are called forward and backward tail chains, according to the time direction considered. Viewing a chain as a tree consisting of a single, long branch, it is natural to seek for generalizations to general Markov trees, i.e. random vectors whose dependence structure is governed by a tree representing a set of conditional independence relations together with a collection of bivariate distributions along the tree edges. As for Markov chains, extremal dependence of such Markov trees can be described in terms of a collection of tail trees, each tree describing the limit distribution of the rescaled Markov tree given that its value at a particular node is large. Moreover, the time-change formula for tail chains generalizes to a relation between these tail trees. Tail trees can be used to compute quantities such as the number of nodes in the graph affected by a shock at a particular node or the probability that a particular part of the graph will be affected by a shock in another part of the graph. Moreover, specifying the graph structure and the bivariate distributions along the edges provides a construction method for max-stable models.