Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange

Maria Letizia Bertotti; Amit K Chattopadhyay; Giovanni Modanese

doi:10.3390/e20030166

Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange

Maria Letizia Bertotti, Amit K Chattopadhyay, Giovanni Modanese

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Abstract

In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum.
The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude.

Original language	English
Article number	166
Number of pages	11
Journal	Entropy
Volume	20
Issue number	3
DOIs	https://doi.org/10.3390/e20030166
Publication status	Published - 5 Mar 2018

Bibliographical note

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Keywords

discretized kinetic theory
wealth exchange models
Langevin stochastic equations
multiplicative noise
Ornstein–Uhlenbeck noise

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10.3390/e20030166Licence: CC BY 3.0

Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Final published version, 1.27 MBLicence: CC BY 3.0

Cite this

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abstract = "In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum.The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude.",

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Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange

Abstract

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Keywords

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