A unified approach to modelling trajectories

The talk will concern the employment of stochastic gradient systems in the modeling and statistical analysis of biological and ecological processes of moving particles. The work is stimulated by scientific questions and data sets of the movements of elk and deer (at the Starkey Experimental Reserve in Oregon), of elephant seals (off the California coast), of Hawaiian monk seals, and of the soccer ball in a game. Stochastic models and data analyses will be presented. The models are motivated by setting down a potential function leading to a stochastic differential equation. The estimated potential function may be used for: simple description, summary, comparison, simulation, prediction, model appraisal, bootstrapping, and employed for estimating quantities of interest. Explanatories, attractors and repellors, may be included in the potential function directly.