Properties of distributions of random variables with independent differences of consecutive elements of the Ostrogradskii series

Authors:
M. V. Prats'ovytyi and O. M. Baranovs'kii

Translated by:
V. Zayats

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **70** (2004).

Journal:
Theor. Probability and Math. Statist. **70** (2005), 147-160

MSC (2000):
Primary 60E05, 26A30; Secondary 11A67, 11K55

DOI:
https://doi.org/10.1090/S0094-9000-05-00638-1

Published electronically:
August 12, 2005

MathSciNet review:
2110871

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Abstract | References | Similar Articles | Additional Information

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

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Additional Information

**M. V. Prats'ovytyi**

Affiliation:
Dragomanov National Pedagogical University, Pyrogov Street 9, Kyïv 01601, Ukraine

Email:
prats@ukrpost.net

**O. M. Baranovs'kii**

Affiliation:
Dragomanov National Pedagogical University, Pyrogov Street 9, Kyïv 01601, Ukraine

DOI:
https://doi.org/10.1090/S0094-9000-05-00638-1

Received by editor(s):
April 11, 2003

Published electronically:
August 12, 2005

Article copyright:
© Copyright 2005
American Mathematical Society