Properties of distributions of random variables with independent differences of consecutive elements of the Ostrogradskiĭ series
Authors:
M. V. Prats’ovytyĭ and O. M. Baranovs’kiĭ
Translated by:
V. Zayats
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
Full-text PDF Free Access
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Abstract: 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.
References
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References
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- T. A. Pierce, On an algorithm and its use in approximating roots of an algebraic equation, Amer. Math. Monthly 36 (1929), 523–525.
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Additional Information
M. V. Prats’ovytyĭ
Affiliation:
Dragomanov National Pedagogical University, Pyrogov Street 9, Kyïv 01601, Ukraine
Email:
prats@ukrpost.net
O. M. Baranovs’kiĭ
Affiliation:
Dragomanov National Pedagogical University, Pyrogov Street 9, Kyïv 01601, Ukraine
Received by editor(s):
April 11, 2003
Published electronically:
August 12, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
