First order Kendall maximal autoregressive processes and their applications

The main idea of this project is construction of distributions and stochastic processes additive in the sense of generalized convolution and application them to modeling environmental conditions. We consider Kendall random walks, for which we solve the problems of the renewal theory, factorization problems and prove limit theorems. The project includes a preliminary study for more advanced problems. This can be used in modeling the dependence between environmental conditions and the number of traffic accidents or medical events (e.g. heart attacks, strokes) or the impact of these conditions on the allergy or asthma. This is the first step to build a short-term forecasts for hospitals, ambulance, police. Hence we assign the project to the KIS 2. Diagnosis and therapy lifestyle diseases and personalized medicine. The results will be published in good international scientistic journals from the JCR list and presented during international conferences.