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Tóm tắt: Stable distributions are really natural asymmetric heavy tailed extensions of normal distributions and have attracted a lot of attention, both in theoretical research and in applied research, especially in finance and risk management studies. The univariate stable distributions are mostly accessible. However, the tools for multivariate stable distributions have been restricted by the lack of closed form expressions for densities and the possible complexity of the dependence structure. We introduce a bijective transformation K=U.T in multidimensional space, that turns a given stable random vector X into a sub-Gaussian random vector Y = K(X). The result provides a theoretical basis of the testing on the stability of multivariate distributions. From that, we propose the procedure of the goodness-of-fit testing on stable distribution of multivariate data and formula to compute density function of stable random vectors.