Abstract:
The theory of branching processes in random environment is an important and rapidly developing part of probability theory. Our talk is mainly devoted to the functional limit theorems for stochastic processes describing various characteristics of the development of populations. Along with traditional conditional limit theorems (with the condition of non-extinction or the condition of attaining a high level) we deal with unconditional limit theorems for branching processes in random environment allowing immigration. An interesting and important feature of the conditional theorems is that the stochastic processes appearing in the limit belong to the class of the so-called conditional Brownian motions (Brownian meander, Brownian excursion, Brownian high jump and so on). These random processes are constructed on the base of Brownian motion and their properties allow to describe many important phenomena of the prelimiting branching processes in random environment.