ABOUT THE APPLICATION OF THE STEIN–TIKHOMIROV METHOD IN THE THEORY OF BRANCHING RANDOM PROCESSES

Galton-Watson branching random processes have many practical applications. When studying the structural and asymptotic structure of these processes, generating functions, characteristic functions, and Laplace substitutions from mathematical apparatus are widely used. In this paper we show the application of a certain method proposed by Charles Stein for proving limit theorems. Studying the speed of convergence in the central limit theorem for stationary quantities satisfying Rosenblat's mixed condition, C. Stein used a certain differential identity for the difference between the corresponding distribution functions. Later, this method of his was modified by A. Tikhomirov in terms of characteristic functions. Currently, this method is called the Stein-Tikhomirov (S-T) method and is widely used in the field of limit theorems.