General limit theorens in probability with applications to statistics.



-The research by Uwe Einmahl focuses on limit theorems of probability in general spaces. Classical probability theory deals mainly with random variables taking values in the real line is well developed, but there are many open questions for random variables taking values in infinite-dimensional spaces. For instance, there is no natural extension of the classical central limit theorem to Banach spaces. Also the so-called law of the iterated logarithm which in the classical setting was established in 1942 has only relatively recently (1986) been obtained for infinite-dimensional spaces. The most recent research by U. Einmahl has addressed not only theoretical questions such as refinements of the basic limit theorems, but also applications to statistics such as density estimation which are possible via so-called empirical processes since these processes can be considered as random elements in a suitable infinite-dimensional space.
Effectieve start/einddatum1/11/9731/12/97

Flemish discipline codes

  • Mathematical sciences