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On problem of singularity of distributions with independent symbols of $F$-expansion

Building: Mykhailo Drahomanov National Pedagogical University

Room: Room C

Date: 2018-09-27 04:45 PM – 17:00

Last modified: 2018-09-22

#### Abstract

The talk is devoted tothe problem of singularity of distributions with independent symbols of $F$-expansion. Such general expansions include $s$-adic expansion, continued fraction expansion, Lueroth, Sylvester, Engel expansions, the second Ostrogradsky expansion and Ostrogradsky-Sierpinski-Pierce expension of real numbers as partial cases. We will show general results on normal properties of $F$-expansion and conditions on singularity of probability measures with independent symbols of $F$-expansion. We also show several examples which demonstrate how these results can be used to prove singularity of famous classes of probability measures generated by Sylvester, $Q^*$, the second Ostrogradskiy, Ostrogradskiy-Sierpinski-Pierce expansions of real numbers.