  Linear stochastic models and discretized kinetic theory are two complementary
analytical techniques used for the investigation of complex systems of economic
interactions. The former employ Langevin equations, with an emphasis on stock
trade; the latter is based on systems of ordinary differential equations and is
better suited for the description of binary interactions, taxation and welfare
redistribution. We propose a new framework which establishes a connection
between the two approaches by introducing stochastic effects into the kinetic
model based on Langevin and Fokker-Planck formalisms. Numerical simulations of
the resulting model indicate positive correlations between the Gini index and
the total wealth, that suggests a growing inequality with increasing income.
Further analysis shows a simultaneous decrease in inequality as social mobility
increases in presence of a conserved total wealth, in conformity with economic
data.
