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2018 New characterizations of the $S$ topology on the Skorokhod space
Adam Jakubowski
Electron. Commun. Probab. 23(none): 1-16 (2018). DOI: 10.1214/17-ECP105


The $S$ topology on the Skorokhod space was introduced by the author in 1997 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.


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Adam Jakubowski. "New characterizations of the $S$ topology on the Skorokhod space." Electron. Commun. Probab. 23 1 - 16, 2018.


Received: 1 September 2016; Accepted: 28 December 2017; Published: 2018
First available in Project Euclid: 9 January 2018

zbMATH: 1390.60120
MathSciNet: MR3749580
Digital Object Identifier: 10.1214/17-ECP105

Primary: 54A10, 54D55, 60B11, 60F17


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