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We study the partial maxima of stationary \alpha-stable processes. We relatetheir asymptotic behavior to the ergodic theoretical properties of the flow. Weobserve a sharp change in the asymptotic behavior of the sequence of partialmaxima as flow changes from being dissipative to being conservative, and arguethat this may indicate a change from a short memory process to a long memoryprocess.

Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes