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The model of anisotropic magnetohydrodynamic turbulence is investigated by the renormalization group approach. It is demonstrated that the inclusion of small anisotropy into the model leads to increasing of the Lorentz force influence. This effect is especially important in the kinetic regime in which the Kolmogorov spectrum of pulsation energy takes place. It is quite different from the isotropic case where the Lorentz force has no influence on large scale properties of magnetohydrodynamic turbulence, even if the external injection of energy is very intensive. Therefore, the magnetic field behaves like a passive admixture. In the anisotropic MHD, nonlinear interactions generate modified "anisotropic Lorentz forces". These forces are relevant for certain values of dimensionless parameter a, which describes the spectrum of the magnetic noise, and the magnetic field ceases to be a passive admixture. In particular, this statement is true for the most realistic value of a = 1 when the random magnetic force amplitude has the same dimensionality as the energy injection rate.

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Heavy-tailed distribution, Exact likelihood ratio test, T-score moment estimator, Insurance, Basel II,

The fully developed turbulence with weak anisotropy is investigated by means of renormalization group approach (RG) and double expansion regularization for dimensions d ≥ 2. Some modification of the standard minimal substraction scheme has been used to analyze stability of the Kolmogorov scaling regime which is governed by the renormalization group fixed point. This fixed point is unstable at d = 2; thus, the infinitesimally weak anisotropy destroyes above scaling regime in two-dimensional space. The restoration of the stability of this fixed point, under transition from d = 2 to d = 3, has been demonstrated at borderline dimension 2 < d c < 3. The results are in qualitative agreement with ones obtained recently in the framework of the usual analytical regularization scheme.

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