Journal of Statistical Physics, Vol. 55, Nos. 3/4, 1989. p. 649-693.
We consider the motion of a heavy mass in an ideal gas in a semi-infinite system, with elastic collisions at the boundary. The motion is determined by elastic collisions. We prove in the Brownian motion limit the convergence of the position and velocity process of the heavy particle to a diffusion process in which velocity and position remain coupled.