Introduction

Abstract

In recent decades a new branch of probability theory has been developing intensively, namely, limit theorems for stochastic processes. As compared to classical limit theorems for sums of independent random variables, the generalizations are going here in two directions simultaneously. First, instead of sums of independent variables one considers stochastic processes belonging to certain broad classes. Secondly, instead of the distribution of a single sum — the distribution of the value of a stochastic process at one (time) point — or the joint distribution of the values of a process at a finite number of points, one considers distributions in an infinite-dimensional function space. For stochastic processes constructed, starting from sums of independent random variables, this is the same as considering the joint distribution of an unboundedly increasing number of sums.