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

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.

Keywords

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