By using the formula first derived by Kirkwood, the friction coefficient of a solvated Brownian particle is determined from the integration on time of the autocorrelation function of the force that the solvent exerts on this particle. Extensive molecular dynamics simulations show that above a definite size of the studied systems the value of the integral defining the friction coefficient goes to a quasiconstant value (a plateau) when the upper bound on time increases. The minimal value of the system size where the integral exhibits this asymptotic behavior, rises with the Brownian particle size. From the plateau, a reliable estimate of the friction coefficient is obtained. (C) 2003 American Institute of Physics.