On movement of Brownian particles along a delaying screen

A two-dimensional Markov diffusion process on the open half-plane as the range of values is considered. With respect to the boundary of the half-plane the process is represented by the normal and tangential components, which are locally independent at any point of the open half-plane. The range of values is extended on the boundary by some rule representing reflection with delaying. Due to this reflection the components of the process become dependent. The tangential component obtains delay as well. The relation between distributions of the initial independent and delayed dependent components is derived in terms of their Laplace images.