  We ascertain the diffusively scaled limit of a periodic Lorentz process in a
strip with an almost reflecting wall at the origin. Here, almost reflecting
means that the wall contains a small hole waning in time. The limiting process
is a quasi-reflected Brownian motion, which is Markovian but not strong
Markovian. Local time results for the periodic Lorentz process, having
independent interest, are also found and used.

Dynamical Systems