Berlin 2005 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 34: Poster
DY 34.14: Poster
Montag, 7. März 2005, 15:30–18:00, Poster TU D
The effect of long-term correlations on the statistics of maxima — •Jan Eichner1, Armin Bunde1, Jan Kantelhardt2, and Shlomo Havlin3 — 1Institut für Theoretische Physik III, Universität Giessen, Germany — 2Fachbereich Physik und Zentrum für Computational Nanoscience, Martin-Luther-Universität Halle-Wittenberg, Germany — 3Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
In common extreme value statistics one assumes that rare extreme events separated by a long time span are statistically independent (Extremal Types Theorem). Here we consider long-term correlated records, where the autocorrelation function C(s) decays as s−γ with 0 < γ < 1. Long-term correlations appear in many natural records, e.g. in temperatures, river flows, heartbeat intervals, and also in financial volatility records. Here we study artificial Gaussian distributed long-term correlated records. The records are segmented in windows of size R. The quantity we are interested in is the maximum-value mi in each window i. We find that the sequence of these maxima is also long-term correlated, such that large maxima are more likely to be followed by large maxima, and small maxima by small maxima. This effect can be clearly seen in the (conditional) distribution of those m-values, that directly follow a fixed m0-value. We show explicitly that the probability for the next event m to be larger than a certain threshold-value M depends significantly on the preceding event m0, an effect that has to be taken into account in any risk estimation.