Preface Issue 3/4-2013

Abstract

The year 2013 is of importance for stochastics in several respects. First of all it is the 250th anniversary of what today is known as Bayes’ theorem. “An essay towards solving a problem in the doctrine of chances” by the late Rev. Mr. Bayes appeared in 1763. Thomas Bruss reviews again the context, the contents, the enormous implications and in parts also the historical discussion of this ground breaking essay. His review originates from the recently established collaboration of Zentralblatt fur Mathematik and Jahresbericht der DMV. 2013 is also “The International Year of Statistics” to which the Jahresbericht contributes with the help of Winfried Stute and his survey on the statistics of point processes and their relations to risk analysis and survival analysis. After having explained the basic notions and ideas by means of simple examples from everday experiences, Winfried Stute focuses in particular on the role of point processes in market research, on modelling of purchase patterns and the influence of advertising and how statistics may help to deal with the a priori unkown model parameters. For about 100 years general relativity has been a strong inspiration both for mathematicians and mathematics. Lorentzian geometry has been established as an active and fast developing field of mathematics which interacts not only with physics but also with other fields of mathematics like e.g. Riemannian geometry. Olaf Muller and Miguel Sanchez give a comprehensible introduction to the key features and an accessible survey on some of the most important and recent developments in Lorentzian geometry. Although there are some common features of Riemannian and Lorentzian geometry, for example the existence and uniqueness of a torsion free covariant derivative, there are however fundamental differences already at a basic level, for example