Skorokhod space and Skorokhod topology in probabilistic considerations during 1956--1999
This paper considers the works devoted to or dealing with sequences of stochastic processes without discontinuities of the second kind and containing functional limit theorems for such processes. The principal consideration is given to the works appearing in the years from 1968-1996 after the famous book of \textit{P. Billingsley} [``Convergence of probability measures'' (1968; Zbl 0172.21201)] was published. General criteria and modifications of the Skorokhod conditions of convergence in \(J_{1}\)-topology and the weak convergence of martingale differences, martingale processes and semimartingales are considered. The conditions of weak convergence of different kinds of processes except processes mentioned above are contained in the paper. Also, the weak convergence of stochastic fields, i.e. the stochastic processes with several parameters, is studied. Citations contain 132 references.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].
scientific article; zbMATH DE number 1620708