Kyurchev D. Probability distributions of random continued fractions and their fractal properties

The thesis is devoted to the investigation of probability distributions with a complicated local structure defined in terms of continued fractions (elementary and non-elementary). We investigated the structure of the distribution, the topological, metric and fractal properties of a random variable represented by the continued fraction whose elements are discretely distributed and take only two values. We also constructed and studied singularly continuous distribution functions of the Cantor type defined by converters of elements of the continued fraction.