  We study a continuous-time version of the Hegselmann-Krause model describing
the opinion dynamics of interacting agents subject to random perturbations.
Mathematically speaking, the opinion of agents is modelled by an interacting
particle system with a non-Lipschitz continuous interaction force, perturbed by
idiosyncratic and environmental noises. Sending the number of agents to
infinity, we derive a McKean-Vlasov stochastic differential equation as the
limiting dynamic, by establishing propagation of chaos for regularized versions
of the noisy opinion dynamics. To that end, we prove the existence of a unique
strong solution to the McKean-Vlasov stochastic differential equation as well
as well-posedness of the associated non-local, non-linear stochastic
Fokker-Planck equation.
