Discrete Sampling of Extreme Events Modifies Their Statistics

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Abstract

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated stochastic process change its EV distribution? We explore this question for correlated random variables modeled via Langevin dynamics for a particle in a potential field. For potentials growing at infinity faster than linearly and for long measurement times, we find that the EV distribution of the discretely sampled process diverges from that of the full continuous dataset and converges to that of independent and identically distributed random variables drawn from the process's equilibrium measure. However, for processes with sublinear potentials, the long-time limit is the EV statistics of the continuously sampled data. We treat processes whose equilibrium measures belong to the three EV attractors: Gumbel, Fréchet, and Weibull. Our Letter shows that the EV statistics can be extremely sensitive to the sampling rate of the data.

Original languageEnglish
Article number094101
JournalPhysical Review Letters
Volume129
Issue number9
DOIs
StatePublished - 26 Aug 2022

Bibliographical note

Publisher Copyright:
© 2022 American Physical Society.

Funding

The support of the Israel Science Foundation via Grant No. 1614/21 is acknowledged.

FundersFunder number
Israel Science Foundation1614/21

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