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

By Gennady Samorodnitsky. 2004

92 citations recorded by the source corpus.

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.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b0cbcff118aeaadf60a748b51787ed389bf2db3d

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In Statistical and Nonlinear Physics

1. Thomas Mikosch
2. Yuwei Zhao
3. Richard A. Davis

Citations in the corpus

• Null flows, positive flows and the structure of stationary symmetric stable processes (2004, methodology): “1 in [20], we obtain the following interesting characterization of processes corresponding to conservative null flows.”
• Measures of serial extremal dependence and their estimation (2013, background): “Stable processes with infinite variance have become popular due to their attractive theoretical and modeling properties; see Samorodnitsky and Taqqu [64].”