Jakubowski, Adam New characterizations of the \(S\) topology on the Skorokhod space. (English) Zbl 1390.60120 Electron. Commun. Probab. 23, Paper No. 2, 16 p. (2018). Summary: The \(S\) topology on the Skorokhod space was introduced by the author in [Electron. J. Probab. 2, Paper 4, 21 p. (1997; Zbl 0890.60003)] and since then it has proved to be a useful tool in several areas of the theory of stochastic processes. The paper brings complementary information on the \(S\) topology. It is shown that the convergence of sequences in the \(S\) topology admits a closed form description, exhibiting the locally convex character of the \(S\) topology. Morover, it is proved that the \(S\) topology is, up to some technicalities, finer than any linear topology which is coarser than Skorokhod’s \(J_1\) topology. The paper contains also definitions of extensions of the \(S\) topology to the Skorokhod space of functions defined on \([0,+\infty)\) and with multidimensional values. Cited in 3 Documents MSC: 60F17 Functional limit theorems; invariance principles 60B11 Probability theory on linear topological spaces 54D55 Sequential spaces 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) Keywords:functional convergence of stochastic processes; \(S\) topology; \(J_1\) topology; Skorokhod space; sequential spaces Citations:Zbl 0890.60003 PDFBibTeX XMLCite \textit{A. Jakubowski}, Electron. Commun. Probab. 23, Paper No. 2, 16 p. (2018; Zbl 1390.60120) Full Text: DOI arXiv Euclid References: [1] Bahlali, K., Elouaflin, A., Pardoux, E.: Homogenization of semilinear PDEs with discontinuous averaged coefficients. Electron. J. Probab.14 (2009), 477-499. · Zbl 1190.60055 [2] Bahlali, K., Elouaflin, A., Pardoux, E.: Averaging for SDE-BSDE with null recurrent fast component. Application to homogenization in a non periodic media. Stochastic Process. 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