[Todos] Seminario de Probabilidad y Estadística Matemática

[Pablo Groisman]

Seminario de Probabilidad y Estadística Matemática.

PROXIMO ENCUENTRO: Miércoles 17 de noviembre, 10:30hs.
EXPOSITOR: Hermann Thorisson, Universidad de Islandia.
TITULO: Coupling and Convergence in Density and in Distribution
LUGAR: Aula de Seminarios, Departamento de Matemática, 2do piso Pabellón 1.

RESUMEN:

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.


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