On the Skorokhod representation theorem

A Survey on Skorokhod Representation Theorem without Separability

Let S be a metric space, G a σ-field of subsets of S and (μn : n ≥ 0) a sequence of probability measures on G. Say that (μn) admits a Skorokhod representation if, on some probability space, there are random variables Xn with values in (S,G) such that Xn ∼ μn for each n ≥ 0 and Xn → X0 in probability. We focus on results of the following type: (μn) has a Skorokhod representation if and only if J...

Integral Representation of Skorokhod Reflection

We show that a certain integral representation of the one-sided Skorokhod reflection of a continuous bounded variation function characterizes the reflection in that it possesses a unique maximal solution which solves the Skorokhod reflection problem.

On the Skorokhod topology

Let E be a completely regular topological space. Mitoma [9 ], extending the classical case E = R 1, has recently introduced the Skorokhod topology on the space D( [0, 1 ] : E). This topology is investigated in detail. We find families of continuous functions which generate the topology, examine the structure of the Borel and Baire a-algebras of D( [0, 1 ] : E) and prove tightness criteria for E...

The Riesz representation theorem

Two Remarks on Skorohod Representation Theorem

With reference to Skorohod representation theorem, it is shown that separability of the limit law cannot be dropped (provided, of course, non separable probabilities exist). An alternative version of the theorem, not requesting separability of the limit, is discussed. A notion of convergence in distribution, extending that of Hoffmann-Jørgensen to non measurable limits, is introduced. For such ...