ABSTRACT
This chapter explores the consideration of the general questions connected with the asymptotic behavior of random sums. Comparing limit laws appearing in these schemes, an attentive reader will notice that in contrast to the classical theory of summation the class of limit distributions for “growing” random sums is not a subclass of the class of limit laws for random sums in the double array scheme. During the last three decades the notion of identifiability of mixtures of probability distribution has been intensively exploited in applied problems connected with separation of mixtures in classification problems, pattern recognition and distribution identification. However, the statistical analysis of real data shows that the increments of the stock price process on relatively short time intervals have distributions different from normal.
