MEAN-FIELD CONTROL VARIATE METHODS FOR KINETIC EQUATIONS WITH UNCERTAINTIES AND APPLICATIONS TO SOCIOECONOMIC SCIENCES

In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of Boltzmann equation to case kinetic models arising in study multiagent systems. For these phenomena, where effect uncertainties is particularly evident, several have been developed whose equilibrium states are typically unknown. particular, aim develop efficient numerical methods based on solving equations phase space by Direct Simulation Monte Carlo (DSMC) coupled sampling random space. To end, exploiting knowledge corresponding mean-field approximation novel Control Variate (MFCV) that able strongly reduce variance standard method We verify observations with examples classical , including wealth exchanges and opinion formation model collective phenomena.