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The local limiting theorem for probability distribution density of random values of an additive quadratic functional over the trajectories of the complex-valued Ornstein-Uhlenbeck process is proved. The additive functional support is extended unlimitedly. A guaranteed estimate of the asymptotic formula derived is given.

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The class frakturK2 of evolutionary equations for axial vector fields on ℝ3 is described. All operators of the class are invariant with respect to space translations in ℝ3, relative to time translations, and they are transformed by covariant way relative to rotations of ℝ3. The class frakturM2⊂frakturK2 of second‐order differential operators is studied such that the corresponding evolution equations have the divergent type and each of them preserves the solenoidal property and the unimodality of the field. The explicit form of such operators is found.