Random phenomena appear in many aspects of our present day world, in its scientific description and its technological and societal transformation. Sometimes as a small perturbation, but sometimes also as a force of great impact. Hence it is not surprising that stochastics, the mathematical theory of random processes, has grown in great strides since its inception by (e.g.) Bachelier (economics), Einstein (physics) and Norbert Wiener (mathematics, information processing) in parallel with the explosion of science and technology in the past century.

The IGK originated at the research center BiBoS (Bielefeld-Bonn-Stochastics) which has been an active contributor to this field of research. In the past 20 years it has hosted hundreds of scientists from all over the world. Collaboration between the two principal investigators of the proposed research training center started in this way -- in 1992 jointly with S. Albeverio they were awarded a Max-Planck research prize for their joint work.

The role of mathematics as a -- computational but also conceptual -- ``toolbox'' for other fields of research is apparent. However, the transfer of results, concepts and models from mathematics to other fields of research is not a one-way flow. Many domains of pure mathematical research have been motivated by questions first posed in a wide variety of ``real world'' disciplines, from the classical example of astronomy to the much more recent one of zoology.

To profit from the inspiration inherent in this lively two-way exchange of ideas we shall link stochastics research with two of its fields of application: Physics and Economics. For both fields it is true that

  • stochastic methods are used importantly

  • they have been, and are, stimulating a considerable amount of mathematical research.

And there is an important third point: the triangle of dialogue partners is closed. In recent years, based on the recognition of a growing amount of jointly used modelling concepts, the dialogue between the two fields of applications is increasingly recognized as being fruitful -- the emerging discipline of "econophysics" underscores this point.