Negadailov P. Limit results on random recurtions

The dissertation is devoted to investigation of asymptotic behaviour of solutions to recurrent equations with random indices, which are naturally appear in three different models. In particular, the asymptotic behaviour of absorbtion times and the number of zero increments in the random walks with a barrier are investigated. Main characteristics of the Bernoulli sieve are found: we provide a criterion of existance of the limiting distribution for properly normalized and centered Un (index of the last occupied interval) in full generality, the same result (undes some additional conditions) is proved for the number of occupied intervals. We have also found the asymptotic behaviour of the number of empty intervals and number of points in the last occupied interval. Also we proved asymptotic results on martingales, related to the branching random walks.