Strong laws under trimming - a comparison between iid random variables and dynamical systems

27.09.2019 15:30 - 16:30

Tanja Schindler (Australian National University, SNS Pisa)

Trimming, i.e. removing the largest entries of a sum of iid random variables,
has a long tradition to prove limit theorems which are not valid if one considers the untrimmed
sum - for example a strong law of large numbers for random variables with an infinite mean.

For certain ergodic transformations, for example piecewise expanding interval maps or subshifts
of finite type, and certain observables over those transformations (regularly varying tails with
exponent strictly between -1 and 0) the results are essentially the same as in the iid case.
The proof in this case is based on an analytic perturbation of the transfer operator.

However, considering the same ergodic transformation and an observable with a different
distribution function, the system can behave completely different to its iid counterpart.
I will give an overview of some of the (sometimes surprising) trimming results in the dynamical
systems setting. This is partly joint work with Marc Kesseböhmer.


H. Bruin, R. Zweimüller

HS 17, 2. OG, OMP 1