  We show how the Smoluchowski dynamics of a colloidal Brownian particle
suspended in a molecular solvent can be reached starting from the microscopic
Liouvillian evolution of the full classical model in the high friction limit.
The integration of the solvent degrees of freedom goes through a multiple time
scale perturbation expansion which removes the secular divergences. A simple
dynamical Monte Carlo scheme is then proposed to solve the resulting evolution
equation for the colloid solute particle. In particular we study the approach
to the equilibrium Boltzmann distribution at late times and its resilience
behavior at shorter times as influenced by the steepness of the external
potential and the friction coefficient around their respective minima. This is
very important to understand the fate of the Brownian particle's random walk
and its evolution history.
