Fixed points of multivariate smoothing transformations

• Applicant: Professor Dr. Matthias Meiners
• Subject Area: Mathematics
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 282184819

In various models of applied probability, the limiting distributions of quantities of interest satisfy recursive distributional equations called fixed-point equations of smoothing transformations, the most prominent example being the convolution equation satisfied by the centered normal distributions. While smoothing transformations and their fixed points have been studied extensively in one dimension, only partial results are available in higher dimensions. The goal of the project is to solve large classes of distributional fixed-point equations in higher dimensions, to understand important features of fixed points such as existence, smoothness and decay of densities or the tail behavior of the survival function, and to apply the theoretical results obtained to classical and recent examples.

• DFG Programme: Research Grants
• International Connection: Austria, France, Poland
• Cooperation Partners: Professor Dr. Dariusz Buraczewski; Professorin Dr. Ewa Damek; Professor Dr. Yves Guivarch; Dr. Konrad Kolesko