A Non-Skorohod Topology on the Skorohod Space

A new topology (called S) is defined on the space D of functions x: [0,1] → R¹ 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 Skorohod's topologies J₁ and M₁. 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 Prohorov's theorems are valid, the a.s. Skorohod representation for subsequences exists and finite dimensional convergence outside a countable set holds.