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A multidimensional Brownian motion with partial reflection on a hyperplane$S$ in the direction $qN+\alpha $, where $N$ is the conormal vector to thehyperplane and $q\in [-1,1], \alpha \in S$ are given parametres, is constructedand this construction is based on both analytic and probabilistic approaches.The joint distribution of $d-$dimensional analogy to skew Brownian motion andits local time on the hyperplane is obtained.

On a multidimentional Brownian motion with partly reflecting membrane on a hyperplane