Principal Investigator: Gyula Pap

The background of our problems are different applied mathematical models including branching processes in biology and epidemiology, integer valued autoregressive models in economics, spatial statistical questions, interest rate models in financial mathematics, etc. The link between our research topics are limit theorems (for probability measures and for stochastic processes as well). Another point is that we separate locally asymptotic (mixed) normal sequences of statistical experiments (leading to asymptotically optimal tests), and the null set of critical parameter values, which is particularly interesting. We are going to determine the asymptotic behavior of supercritical multitype branching processes and the estimators of their parameters on the critical surface. In case of the extremal points we have to derive limit theorems with exotic limit distributions. In these cases one should apply unusual scalings as well. Our intended results are steps towards a better understanding of the statistical behavior of complex random systems with branching phenomena, such as affine processes. Allowing time inhomogeneity is also of great importance. Under low moment assumptions a new technique based on random measures is needed. We are also intend to investigate problems that are at the cross-roads of Stochastic Geometry and the Brunn-Minkowski theory of convex bodies. Random geometric structures have a natural connection to convexity and to integral geometry via a long history. We plan to study geometric properties of random intersections of balls and random polytopes in various spaces under different distributional conditions.