Properties of distributions of random variables with independent differences of consecutive elements of the Ostrogradskii series
Mykola V. Pratsiovytyi, O. M. Baranovs’kiĭ · Theory of Probability and Mathematical Statistics · 2005
Several metric relations for representations of real numbers by the Ostrogradskiĭ type 1 series are obtained. These relations are used to prove that a random variable with independent differences of consecutive elements of the Ostrogradskiĭ type 1 series has a pure distribution, that is, its distribution is either purely discrete, or purely singular, or purely absolutely continuous. The form of the distribution function and that of its derivative are found. A criterion for discreteness and sufficient conditions for the distribution spectrum to have zero Lebesgue measure are established.