Extremal theory for long range dependent infinitely divisible processes
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Abstract
We prove limit theorems of an entirely new type for certain long memory
regularly varying stationary \id\ random processes. These theorems
involve multiple
phase transitions governed by how long the memory is. Apart from one
regime, our results exhibit limits that are not among the
classical extreme value distributions. Restricted to the one-dimensional
case, the distributions we obtain interpolate, in the appropriate
parameter range, the