Seminarium i matematisk statistik
onsdagen den 3 maj 15.15 i MH:227

Hermann Thorisson
Science Institute
University of Iceland, Reykjavik

Title:
Coupling

Abstract:
Coupling means the joint construction of two or more
random elements. The aim is usually to establish some
distributional relation between the individual elements.
But the aim can also be the reverse: to turn a distributional
relation into a pointwise relation. Examples are the
turning of stochastic domination into pointwise domination,
weak convergence into pointwise convergence, and liminf
convergence of densities into pointwise convergence where the
random elements actually hit the limit. This deepens our
understanding of the distributional relation itself, may enable
us to establish previously hard-to-prove facts by simple pointwise
arguments, and often leads to unexpected new results.

This talk starts off with the above examples and then moves to
stochastic processes (exact coupling, shift-coupling, and
epsilon-couplings). Applications to Markov Processes, Regenerative
Processes and in Palm Theory will be indicated. The view is then
extended to random fields with applications in Palm Theory, and
finally to random elements under a topological transformation group
which opens up many new possibilities for applications:
self-similarity, exchangeability, rotational invariance, the Lorentz
and Poincaré transformations, ...

Reference:

Thorisson, H. (2000). Coupling, Stationarity, and Regeneration.
                  Springer, NY.