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Peculiarities of the large numbers law in conditions of disturbances of statistical stability are studied. It is shown that for random sequences the sample mean may converge to a finite number, converge to positive or negative infinity or fluctuate in a fixed interval. A series of theorems are proven, which describe the large numbers law for hyper-random sequence. It is demonstrated that the sample mean in case of a hyper-random quantity may converge to a finite number, converge to a set of finite numbers, fluctuate in non-intersecting intervals of conditional boundaries, fluctuate in unconditional boundaries interval or converge to positive or negative infinity. Differences in convergence types of random and hyper-random sequences should be accounted for when studying radio-engineering devices and systems.

The known ways of representing hyper-random quantities and processes are analyzed with respect to the appropriateness of their application to describe various types of transformations. A series of relations between characteristics and parameters of transformed and initial hyper-random quantities and processes is obtained. Recommendations on the use of various ways of representing scalar and vector hyper-random quantities in the cases of linear and non-linear transformations as well as processes subject to non-inertial and inertial transformations are given.