Darbe nagrinėjami taškiniai procesai (nehomogeninis Puasono procesas ir atstatymo procesas), randamos bendrosios sąlygos, kad būtų patenkintas lokalus asimptotinis normalumas. / The purpose of this work is to determine general conditions for local asymptotic normality to be assured.The point processes (renewal process and non-homogenous Poisson process) and their properties are examined in the first part of work. Then the conditions for the local asymptotic normality have been investigated. In the second part of work it is shown how these conditions are satisfied in the cases of the renewal process and non-homogenous Poisson process.

The novelty and originality of the work consists in the fact that in order to obtain asymptotic expansions with optimal values of the remainder terms in the zone of large deviations, along with the cumulant method the classical method of characteristic functions has to be used. In addition, when solving the problems stated in the work, other than the well known results in the problems of limit theorems of the probability theory and mathematical statistics, we have to estimate constants. Technically it is frequently rather a complicated task. The results obtained in the work have good opportunities to be applied in probability theory, mathematical statistics, econometric, etc. That is illustrated in the last section of the work in which theorems of large deviations are proved in the summation of weighted random variables with weights as well as discounted limit theorems.