The principal investigator will continue the study of measure-valued population processes and multi-level branching diffusions. The major motivation for the project is to create models to fit the hypothesis and then to use the acceptable models to predict the future behavior. The classes of stochastic processes to be studied have been shown as appropriate models for analysis of allelic frequency data. Measure-valued branching processes trace not only the numbers of particles but also their distributions over the time. Thus the measure-valued aspect of the processes make them particularly attractive models in epidemiological spread of communicable disease or economic wealth of various populations. Mathematically, the stochastic measure diffusion process is the continuous analogue of an infinite particle branching Markov system. The project will address three specific aspects of these processes: properties of the topological support of the associated random measure, including the coherence or dispersiveness, clustered nature or scatteredness, and singularity or absolute continuity of such random measures.
