Distribution of values of classic singular Cantor function of random argument

DOI10.1515/rose-2018-0016zbMath1440.11147OpenAlexW2892100537MaRDI QIDQ1756023

Iryna Lysenko, Oksana Voitovska, Mykola V. Pratsiovytyi

Publication date: 11 January 2019

Published in: Random Operators and Stochastic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/rose-2018-0016

zbMATH Keywords

discrete probability distribution\(s\)-adic representation of numbersLebesgue structure of probability distributionmixture of discrete and continuous probability distributionsrandom variable with independent ternary digitssingular Cantor function

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Singular functions, Cantor functions, functions with other special properties (26A30) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Continuity and singularity of induced measures (60G30)

Related Items (1)

Distribution of Values of Cantor Type Fractal Functions with Specified Restrictions

Cites Work

• Singularity of the digit inversor for the \(Q_3\)-representation of the fractional part of a real number, its fractal and integral properties
• On the origin of the phase-space diffusion limit in (dis)ordered protein aggregation
• Self-affine singular and nowhere monotone functions related to the \(Q\)-representation of real numbers
• An Increasing Continuous Singular Function
• Convolutions of distributions of random variables with independent binary digits
• Random Variables with Independent Binary Digits
• On Some Singular Monotonic Functions Which Are Strictly Increasing
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