From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic...

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Bibliographic Details
Published in:Journal of statistical physics 2018-05, Vol.171 (3), p.434-448
Main Author: Nazé, Pierre
Format: Article
Language:English
Subjects:
Bivariate analysis
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Computer simulation
COMPUTERIZED SIMULATION
COUPLING
DISTRIBUTION
Economic models
Extreme values
Mathematical and Computational Physics
Mathematical models
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Random variables
RANDOMNESS
Statistical analysis
Statistical distributions
Statistical inference
Statistical Physics and Dynamical Systems
Theoretical
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Summary:Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel–Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag–Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-018-1999-8