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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72773We 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.Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000261Probability60G10, 37A40 (Primary)Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processestext