Wednesday, May 4, 2022 - 14:00 in V3-201 + Zoom
On fractal properties of probability distributions generated by Cantor series
A talk in the Bielefeld Stochastic Afternoon series by
Olha Dorosh
| Abstract: |
The talk is devoted to fractal properties of distributions of random
variables
$$\xi = \sum\limits_{k=1}^\infty \frac{\xi_k}{n_1 n_2 \ldots n_k},$$
where $\{n_k\}$ is a fixed sequence of positive integers, $n_k \geq
2$, and $\xi_k$ are independent random variables taking values $0,
1,..., n_k-1$ with probabilities $p_{0k}, p_{1k},..., p_{n_k-1,k}$.
In particular, we shall discuss the problem of comparability (w.r.t.
Hausdorff measure) of net measures generated by Cantor series
expansions; faithfulness of underlying Vitaly covering.
We shall also discuss some open problems related to fractal properties
of spectra $S_\xi$, DP-properties of $F_\xi$, and fine fractal
properties of $\mu_\xi$.
Within the CRC this talk is associated to the project(s): A5, B1 |
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