## Hermann Þórisson (11/10/16)

Math Colloquium

### Speaker: Hermann Þórisson

Title: On the Skorohod Representation

Location: Naustið, Tæknigarði

Time: Tuesday, Ocober 11, 12:30-14:00

### Abstract:

According to the Skorohod representation theorem, convergence in distribution to a limit in a separable set is equivalent to the existence of a coupling with elements converging a.s. in the metric. A density analogue of this theorem says that a sequence of probability densities on a general measurable space has a probability density as a pointwise lower limit if and only if there exists a coupling with elements converging a.s. in the discrete metric. In this talk the discrete-metric theorem is extended to stochastic processes considered in a widening time window. The extension is then used to prove the Skorohod representation theorem.