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Anomalous diffusion in non-Markovian walks having amnestically induced persistence.

A S Ferreira¹, J C Cressoni, G M Viswanathan

¹Instituto de Física, Universidade Federal de Alagoas, Maceió 57072-970, AL, Brazil.

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

|April 7, 2010

Summary

This study estimates the Hurst exponent for non-Markovian walks with memory effects. Results show log-periodic oscillations with significant memory loss and explore fractal memory patterns, impacting central limit theorem conditions.

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Area of Science:

* Statistical Physics
* Complex Systems Analysis
* Time Series Analysis

Background:

* Non-Markovian processes exhibit memory, deviating from the Markovian assumption of independence.
* The Hurst exponent quantifies long-term memory and self-similarity in time series.
* Previous research links log-periodic oscillations to memory loss in such walks.

Purpose of the Study:

* To numerically and analytically estimate the Hurst exponent for non-Markovian walks with amnestically induced persistence.
* To investigate the Hurst exponent in non-Markovian walks featuring diluted memory.
* To analyze walks with fractal memory patterns (Thue-Morse, Fibonacci) and their relation to the central limit theorem.

Main Methods:

* Numerical estimation of the Hurst exponent.
* Analytical calculation of the Hurst exponent.
* Simulation of non-Markovian walks with varying memory characteristics.

Main Results:

* Estimated Hurst exponent values are consistent with prior findings on memory loss and log-periodic oscillations.
* Numerical estimates for diluted memory non-Markovian walks were obtained.
* Analysis of Thue-Morse and Fibonacci fractal memory patterns was performed.

Conclusions:

* The study provides insights into the Hurst exponent's behavior in complex memory-dependent systems.
* Findings contribute to understanding the conditions under which the central limit theorem applies to non-Markovian processes.
* The characterization of memory effects is crucial for modeling real-world phenomena.