2005
DOI: 10.1090/s0094-9000-05-00638-1
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Properties of distributions of random variables with independent differences of consecutive elements of the Ostrogradskii series

Abstract: Abstract. Several metric relations for representations of real numbers by the Ostrogradskiȋ type 1 series are obtained. These relations are used to prove that a random variable with independent differences of consecutive elements of the Ostrogradskiȋ 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… Show more

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