Limit theorems with refinements for random processes

One considers the problem of the derivation of limit theorems with refinements in functional spaces. One proves theorems on the expansions of the mathematical expectations of bounded continuous linear functionals of the trajectories of a Gaussian random process. From these theorems one derives a limit theorem with correction terms for the mathematical expectation of a functional of the trajectories of the time-discretized Wiener process, when the step of the discretization tends to zero. One discusses questions regarding generalizations, methods of proof, and the relation of these kind of limit theorems with other problems of the theory of probability, as well as possible applications of these theorems.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 94–114, 1986.