Reflecting Brownian motion in $d$-ball

Following the works of I. A. Ibrahimov, N. V. Smorodina and M. M. Faddeev, we develop a new construction of the Brownian motion with reflection in $d$-ball. The main advantage of our new approach is that it allows one to construct reflecting Levy processes, whereas previous constructions are limited to diffusion processes. In our upcoming work we shall extend the results to the symmetric Levy processes in a smooth domain.