Scaling in Stochastic Models – Scaling in Stochastic Models is a research project funded by Coratian Science Foundation.

Abstract

Stochastic models are of great importance in describing numerous phenomena in various fields of science and life. An essential property of time-dependent models is their behavior under time and space scaling. The characteristics of many phenomena can be significantly changed by changing the scale. For example, as we move from the tiny world of particles to the astronomical scales, the laws of nature may behave drastically different. The need for models with specific scaling properties comes from numerous practical applications in medicine, biology, physics, finance, economics and other fields of science. The goal of the project is the construction and investigation of stochastic models with special scaling properties. The emphasis is placed on the study of properties of models in the limits of small or large scales. Among other results, a possible explanation will be provided for the phenomenon related to the scaling of empirical moments, known as Taylor's law. By replacing the time scale of some standard processes, the new classes of stochastic processes will be constructed and analyzed. These new models will be applied in epidemiology and EEG signal analysis. Furthermore, model for the classification of neurocognitive outcomes based on scaling parameters will be developed.

Duration: December 15, 2023 - December 14, 2027