| Abstract [eng] |
In this thesis, we studied distribution functions obtained by randomly stopping minimum, maximum, minimum of sums and maximum of sums of random variables. Primary random variables are considered to be real-valued, independent and possibly differently distributed. The random variable defining the stopping moment is integer-valued, nonnegative and not degenerate at zero. We have found conditions when the distribution functions of these randomly stopped structures belong to the class of generalized subexponential distributions. The belonging of the distributions of randomly stopped structures to the class of generalized subexponential distributions can be determined either by primary random variables or by counting random variables. In this thesis, we have considered the case when a set of primary random variables has a decisive value. The primary random variables considered in all theorems can be differently distributed. However, additional conditions of all theorems are satisfied in the case where the primary random variables are identically distributed. We also have found the conditions on the primary random variables, under which the randomly stopped structures are either heavy-tailed or light-tailed. Our main results are formulated in Theorems . |
