Skorokhod space and Skorokhod topology in probabilistic considerations during 1956--1999
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.60007
publication date: 2001-07-16T00:00:00Z
Mathematics Subject Classification ID: 60B10
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 1620708
zbMATH Keywords: convergence of probability measures
zbMATH Keywords: Skorokhod topology
zbMATH Keywords: stopping time
zbMATH Keywords: martingale
zbMATH Keywords: Markov and diffusion processes
zbMATH Keywords: stochastic fields
author: Yuliya S. Mishura
MaRDI profile type: Publication
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title: Skorokhod space and Skorokhod topology in probabilistic considerations during 1956--1999
review text: 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].
description: scientific article; zbMATH DE number 1620708