All phenomena in science and society are ruled by randomness, sometimes partially or to a considerable extent. The branches of mathematics that enable us to understand, predict and control such phenomena are Probability Theory, Statistics, Stochastic Operations Research and Financial Mathematics. Collectively they go by the name Stochastics. All aforementioned branches are represented within the stochastics programme at the Korteweg-de Vries Institute.
Probability Theory studies the behaviour of a stochastic system of which the underlying chance mechanism is known: given this chance mechanism certain system characteristics are analyzed. Probability Theory is rooted in Analysis, more specifically in Measure and Integration Theory, and it nourishes the other branches of Stochastics.
Observing the behaviour of a stochastic system of which the underlying chance mechanism is unknown, one may try to induce which is the true underlying chance mechanism. The mathematics of this problem is called Mathematical Statistics. Our statistics research is motivated by both theoretical issues and by problems raised in application areas.
Topics of a theoretical nature are found in nonparametric and semiparametric statistics, as well as in Bayesian statistics. Applied research is motivated by statistical problems in e.g. finance, neuroscience, systems biology, and forensic science.
Some of the staff working within the Stochastics research programme are also involved with the Gravitation Programme NETWORKS.