Probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in $d$-hyperball

We extend the construction of probabilistic representations for initial-boundary value problem solutions to the non-stationary Schrödinger equation in d-hyperball first obtained in the works by I. Ibragimov, N. Smorodina and M. Faddeev to a multidimensional case. Further on, we show that in these representations the Wiener process could be replaced by a random walk approximation. The $L_2$-convergence rates are obtained.