Probability Seminar by Anita Winter
Representation theorems for historical interacting
Fisher-Wright diffusions
We consider spatially interacting Moran models and
their diffusion limit which are interacting
Fisher-Wright diffusions. For both models the historical
process is constructed, which gives information about
genealogies. For any fixed time, particle representations
for the historical process of a collection of Moran models
with increasing particle intensity and of the limiting
interacting Fisher-Wright diffusions are provided
on one and the same probability space by means of
a look-down process.
It will be discussed how this can be used to obtain
new results on the long term behavior. In particular, we give
representations for the equilibrium historical processes.
Based on the latter the behavior of
large finite systems in comparison with the infinite system
is described on the level of the historical processes.
The talk is based on joint work with Andreas Greven and
Vlada Limic.