Jakubowski, Adam A non-Skorokhod topology on the Skorokhod space. (English) Zbl 0890.60003 Electron. J. Probab. 2, Paper 4, 21 p. (1997). Summary: A new topology (called \(S\)) is defined on the space \(D\) of functions \(x: [0,1] \to R^1\) which are right-continuous and admit limits from the left at each \(t > 0\). Although \(S\) cannot be metricized, it is quite natural and shares many useful properties with the traditional Skorokhod’s topologies \(J_1\) and \(M_1\). In particular, on the space \(P(D)\) of laws of stochastic processes with trajectories in \(D\) the topology \(S\) induces a sequential topology for which both the direct and the converse Prokhorov’s theorems are valid, the a.s. Skorokhod representation for subsequences exists and finite-dimensional convergence outside a countable set holds. Cited in 2 ReviewsCited in 22 Documents MSC: 60B05 Probability measures on topological spaces 60F17 Functional limit theorems; invariance principles 60G17 Sample path properties 54D55 Sequential spaces Keywords:Skorokhod space; Skorokhod representation; convergence in distribution; sequential spaces; semimartingales PDF BibTeX XML Cite \textit{A. Jakubowski}, Electron. J. Probab. 2, Paper 4, 21 p. (1997; Zbl 0890.60003) Full Text: DOI EMIS EuDML