Hermann Þórisson, University of Iceland,

Location :

Ecole Normale Supérieure
45 rue d'Ulm
75005 Paris

within the team of TREC, in the main building of the direction, 2nd floor.
Access: http://www.di.ens.fr/AccesDI.html

Abstract :

According to Dudley's extension of the Skorohod representation theorem, convergence in distribution on a separable metric space 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 lower pointwise limit if and only if there exists a coupling with elements converging a.s. in the discrete topology. In this talk the latter result is extended to discrete-topology convergence of stochastic processes in a widening time-window. An relatively elementary version of that result is then used to prove the Skorohod-Dudley theorem.

Host :

Ecole Normale Supérieure