Approximation Methods in Probability Theory

Abstract

Preface The limit theorems of probability theory are at the core of multiple models used in the broad field of scientific research. Their main function is to replace the initial complicated stochastic model of a phenomenon by its somewhat simpler approximate substitute. As a rule, such substitute is easier to use since its properties are well known. However, it raises a key question: how good is the approximation? For example, even in the famous central limit theorem, the rate of convergence to the normal law can be extremely slow. Therefore, it is important to measure the magnitude of the difference between models or, in other words, to estimate the accuracy of approximation. However, there is a notable lack of books that are specifically focused on teaching how to do it. One could find numerous monographs and textbooks devoted to approximations, especially related to the central limit theorem, but the prime concern of their authors is the impressive results, not the methods that are used in the process. Thus, such books rarely involve more than one method, not to mention an actual compa rison of the applicability of several approaches.