Про лебегівську структуру розподілу одного випадкового степеневого ряду, представленого $s$-ковим дробом / On the Lebesgue structure of distribution of random power series in the form of $s$-adic representation

Abstract: У доповіді розглядається випадкова величина \[ \xi = \sum_{k=1}^\infty \frac{\xi_k}{s^k}, \] де $2 \leq s \in \mathbb{N}$, $(\xi_k)$ — послідовність незалежних випадкових величин, причому кожна з величин $\xi_k$ набуває $s$ цілих значень, які утворюють повну систему лишків за модулем $s$. Представлені критерії належності розподілу $\xi$ до кожного з трьох чистих типів розподілу.

In the talk, we consider a random variable \[ \xi = \sum_{k=1}^\infty \frac{\xi_k}{s^k}, \] where $2 \leq s \in \mathbb{N}$, $(\xi_k)$ is a sequence of independent random variables, and any $\xi_k$ takes $s$ integer values that form a complete residue system modulo $s$. Criteria for distribution of $\xi$ to be of every pure Lebesgue type of probability distribution are given.

Ukrainianprobability

Audience: researchers in the discipline

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Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable

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