A. V. Skorokhod's investigations in the area of limit theorems for random processes and the theory of stochastic differential equations (Q1814607)

This is a survey of basic ideas and results of A. V. Skorokhod in the indicated fields. In the first section the development from Donsker's invariance principle to Skorokhod's spaces of functions and Skorokhod's method of ``a single probability space'' are explained. Applications of the methods to special classes of processes are mentioned. The explanation of the method of embedding random variables into a Wiener process finishes the section. The other section is devoted to stochastic differential equations. Skorokhod's extension of the theory of Itô and Gikhman is mentioned. Among others the achievements in the following areas of problems are explained: existence and uniqueness problems, descriptions of Markov processes by stochastic differential equations, connections of linear equations and stochastic semigroups, etc.