On spectral gap properties and extreme value theory for multivariate affine stochastic recursions
Résumé
We consider a general multivariate affine stochastic recursion and the associated Markov chain on R d. We assume a natural geometric condition which implies existence of an unbounded stationary solution and we show that the large values of the associated stationary process follow extreme value properties of classical type, with a non trivial extremal index. The proof is based on a spectral gap property for the action of the corresponding Markov operator on spaces of regular functions with slow growth, and on the clustering properties of large values in the recursion.
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