We study the partial maxima of stationary α-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.
"Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes." Ann. Probab. 32 (2) 1438 - 1468, April 2004. https://doi.org/10.1214/009117904000000261