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A non-Skorokhod topology on the Skorokhod space. (English) Zbl 0890.60003
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.

MSC:
60B05 Probability measures on topological spaces
60F17 Functional limit theorems; invariance principles
60G17 Sample path properties
54D55 Sequential spaces
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