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Memory effects in recurrent and extreme events.

C Nicolis¹, G Nicolis

¹Institut Royal Météorologique de Belgique, 3 Avenue Circulaire, 1180 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 7, 2010

Summary

This study introduces a dynamical approach to understand recurrent and extreme events by analyzing correlations and memory in probability distributions. It reveals significant differences from classical statistical theories for independent random variables.

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Area of Science:

Dynamical systems theory
Statistical physics
Probability theory

Background:

Recurrent and extreme events are crucial in various scientific domains.
Classical statistical theory often assumes independent and identically distributed variables, which may not capture complex event dynamics.
Understanding the influence of correlations and memory is essential for accurate modeling.

Purpose of the Study:

To develop a dynamical approach for analyzing recurrent and extreme events.
To investigate the role of correlations and memory in probability distributions and their moments.
To compare the dynamical approach with classical statistical theory.

Main Methods:

Developed a dynamical framework to analyze event dynamics.
Applied the procedure to various systems including Markov chains (first and second order, homogeneous, non-Markovian, nonhomogeneous) and deterministic dynamical systems.
Focused on the structure of probability distributions and their low-order moments.

Main Results:

Identified substantial differences between the dynamical approach and classical statistical theory.
Demonstrated the importance of correlations and memory in shaping event characteristics.
The approach is applicable to a range of stochastic and deterministic systems.

Conclusions:

A dynamical perspective offers a more comprehensive understanding of recurrent and extreme events than classical statistical methods.
Correlations and memory are key factors influencing the behavior of these events.
The developed procedure provides a robust framework for analyzing complex event dynamics across different systems.