Математика институти

ABSTRACT of DSc Dissertation

Urgency and demand of the dissertation topic. The theory of stochastic branching processes is an area of modern probability theory that provides appropriate mathematical models to describe the probabilistic evolution of many natural and technical phenomena connected with population growth. Appearing as a special scientific field in the forties of the twentieth century, this theory, due to the applied and descriptive nature of the explored problems and phenomena, is a well developed and one of active scientific areas with theoretical interests and practical applications. The theory of branching processes has applied successfully in various fields and by present time, it has made important contributions to theoretical physics, molecular biology, chemistry, demography, medicine and to many other areas of applied science.
At present, the spectrum of applications of the theory of the branching processes is still expanding. It covers in particular, the description of the probabilistic evolutions of various biological populations, the study of the problems of the queuing theory and many other problems of current interest. The advancement of this theory, on the one hand is due to the demand for an in-depth study of classical models and, on the other hand, it occurs due to the creation of new particle transformation schemes that deeply and clearly describe the essence of the real phenomena under studying. In this context, the gradual improvement of the available results within of the classical models and research aimed to establish new results that most correspond to the natural conditions is urgent task.
The foregoing gives reason to assert that the research conducted on the topic of dissertation is relevant and important from the point of view of applications.