Marynych O. Random recursvie sequences

The thesis is devoted to the analysis of random recursive structures by means of random recursive sequences. A new technique is developed for the asymptotic analysis of moments of linear random recurrences which is called the method of iterative functions. Using the method of moments some general results for the weak convergence of the absorbtion time in non-increasing Markov chains are proved. In the second part of the thesis we present some new results for two models where random recursive sequences arise: the Bernoulli sieve and exchangeable coalescents.