*Programme leaders: F.M.Dekking, W.Th.F.den Hollander*

Research in this programme is carried out in a very broad range of topics, covering most of the aspects of the mathematical discipline of probability theory and its applications to other mathematical areas, other sciences, and industry and technology. The basic themes of the research comprise among others extreme value theory and applications, optimal stopping, infinitely divisible distributions, stochastic recurrence, stochastic geometry, percolation and particle systems, modelling and simulation of geological structures, branching processes, queueing theory and applications, diffusions, ergodic theory, stochastic dynamical systems, fractal geometry and coding, noncommutative probability theory, stochastic inequalities, and simulation.

Probability theory and its applications develops mathematically precise models for quantitatively describing uncertain situations, and applies these models in order to arrive at optimal or nearly optimal decision procedures. Research carried out in this domain in The Netherlands, and in particular in the Stieltjes Institute, is broad-ranging. Inside of the Institute, there are common interests and collaborations with the programmes Statistics, Stochastic Operations Research, Topology and Dynamical Systems and Number Theory.