Spatial-temporal point processes and their applications

The project is devoted to basic research in mathematics, probability and statistics, with applications to neurophysiology and economics. A broad new class of random point processes in space and time will be developed and its properties investigated mainly analytically and also by means of simulations. Advanced probabilistic tools will be enhanced to solve complex modeling problems. Various statistical questions arise to achieve inference of these models. Parametric and semi-parametric methods will be developed to this purpose, the admissibility of estimators will be studied. Classical, Bayes and Monte Carlo techniques will be enhanced. Spike trains of animal's neurons will be modeled by spatial-temporal point processes, prediction and filtration problems will be solved. Various estimators of characteristics will be compared using real data in this situation. The project will be solved in four cooperating workplaces, by partly engaged researchers and PhD students within five years.