## 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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