3.1. ProbabilityProgramme leaders: W.Th.F. den Hollander, R.W.J. Meester
Description of the programme.
Probability theory is a branch of mathematics with a strong intuitive content. The mathematical theory of stochastics has been developed and is being developed in order to understand and deal with random phenomena in the world around us. So, apart from the autonomous development of the field strong emphasis is placed on interaction with other disciplines where random phenomena play an important role. The latter aspect is prominent in the research in the Netherlands and particularly in the Stieltjes Institute. There are common interests and collaborations with the programmes Statistics, Stochastic Operations Research, Topology and Dynamical Systems and Number Theory.
Status of the programme.
The research in the Stieltjes programme Probability Theory will be concentrated in the following areas:
The research in ergodic theory and dynamical systems of the group has significant impact in analysis, number theory, and fractal geometry. Similarly, the research in extreme value theory, heavy tailed models and infinitely divisible distributions has applications in statistics, research in optimal stopping and queueing theory in operations research, research on fractal geometry, ergodic theory, percolation and particle systems in mathematical physics, research on stochastic differential equations and modelling of stochastic processes in the theory of financial mathematics and the research on branching processes in computer science.
- ergodic theory and dynamical systems
- extreme value theory, heavy tailed models and infinitely divisible distributions
- optimal stopping and queueing theory
- fractal geometry, percolation and particle systems
- stochastic differential equations and modeling of stochastic processes
- branching processes.