9625753 Adler ABSTRACT Super Brownian motion (SBM), currently one of the hottest topics in Probability Theory, is what one gets by renormalising an infinite number of branching Brownian motions. It is of intrinsic interest to probabilists, and of more general interest because of ties to PDE theory, and because it may turn out to be a very important process for modeling purposes and as a building block from which other measure valued processes can be constructed. This project is primarily aimed at seeing how well SBM indeed serves as such a building block, by investigating a number of other infinite dimensional stochastic processes that can be built either from SBM or from simple variants of it. The first example that will be tackled is a ``super iterated Brownian motion'' that seems to be accessible to this approach and yet is a stochastic process which promises a lot of surprises in its structure and behavior. As a modeling tool, the random processes that will be studied in this project have applications to a wide diversity of different fields. They provide good models for studying the development of genetic diversity over a large number of generations, and, indeed, it was as models here that superprocesses originally developed. In this and related projects, the PI and his colleagues will also be using superprocesses to study the dispersion of mass via ocean currents. It is hoped that the models developed will lead to a better understanding of the statistical aspects of, for example, the spread of ocean pollutants. Another side benefit will be the study of the spatial structure of populations of small ocean dwelling organisms such as plankton, a topic of both ecological and defense (radar) interest.
