On the convergence to a multidimensional stable law of the distribution of a location parameter for the composition of random motions in Euclidean space

We consider a distribution of a location parameter for the composition of random motions in the Euclidean space. It is supposed that the $n$-fold convolution of rotation parameter distribution converges weakly to the uniform distribution on $SO(d)$ and that the location parameter has a distribution belonging to the domain of attraction of some nondegenerate multidimensional law. The integral limit theorem for the location parameter is proved.