Maxmoments and mixing in stochastic systems
by Dr Daniel Tokarev
Abstract: We consider the expectations of the maxima of independent non-negative
random variables. In the case of identically distributed random variables,
when such expectations are referred to as maxmoments, we solve an analogue
of the moment problem and present the asymptotics of the maxmoments as the
number of random variables increases to infinity, and give an application
to simple branching processes. In the case of non-identically distributed
independent random variables, we derive tight upper and lower bounds for
these expectations in terms of the maxmoments (which, incidentally, is
equivalent to deriving tight bounds for the L 1-distance between the
arithmetic and geometric means of the respective distribution functions).
We also investigate a related optimization problem in the case when the
random variables can follow one of two fixed different distributions.
(This talk is based on joint research with K. Hamza, A. Sudbury, F.
Klebaner and P. Jagers.)
For More Information: Konstantin Borovkov K.Borovkov@ms.unimelb.edu.au