A Langevin approach to the Log–Gauss–Pareto composite statistical structure

Iddo I. Eliazar and Morrel H. Cohen

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 22, 5598-5610

Abstract: The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.

Keywords: Ornstein–Uhlenbeck dynamics; Linear forces; Gauss distribution; Langevin dynamics; Sigmoidal forces; Exponential tails; Geometric Ornstein–Uhlenbeck dynamics; Log–Gauss distribution; Geometric Langevin dynamics; Power-law tails; Laplace distribution; Log–Laplace distribution; ‘‘mild” randomness; ‘‘wild” randomness; Universality (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:22:p:5598-5610

DOI: 10.1016/j.physa.2012.06.024

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