New characterizations of the S topology on the Skorokhod space

2016/09/01 by Jakubowski, Adam · 1 citation
#54A10 #54D55 #60B11 #60F17 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1609.00215

Abstract

The S topology on the Skorokhod space was introduced by the author in 1997 and since then it 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 compact description, exhibiting the locally convex character of the S topology. It is also shown that S is, up to some technicalities, finer than any linear topology which is coarser than Skorokhod's J₁ topology. The paper contains also definitions of extensions of the S topology to the Skorokhod space of functions defined on [0,+∞) and with multidimensional values.

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