Peculiarities of the large numbers law in conditions of disturbances of statistical stability
Игорь Ильич Горбань · Radioelectronics and Communications Systems · 2011
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.