Analysis of Noise and Causal Dependence in Stochastic Dynamical Systems

PhD study program: Applied Mathematics
Akademic year: 2026-2027
Advisor: Mgr. Jozef Jakubík, PhD. (jozef.jakubik@savba.sk)
External educational institution: Institute of Measurement Science SAS
Accepting university: Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Department of Applied Mathematics and Statistics

Annotation:

The analysis of causal relationships in dynamical systems is a research problem with a wide range of application areas, including neurophysiological measurements, climate data, economic indicators, and other complex systems. Current research in this field is mainly focused on deterministic dynamical systems or on autoregressive models. The next step is the extension of existing approaches to stochastic dynamical systems, which combine deterministic dynamics with stochastic influences inherent in real-world measurements. The reliability of existing methods for causality detection, such as approaches based on cross-mapping, transfer entropy, and related techniques, will be analysed using time series generated by stochastic dynamical systems, with the aim of identifying the limits and constraints of these methods. Based on the obtained results, modifications and generalisations of the methods will be proposed to better reflect the stochastic nature of the studied systems and to improve the robustness of causal analysis. The topic is suitable for graduates with an interest in the application and further development of mathematical approaches in data analysis and dynamical systems. Requirements include proficiency in technical English and knowledge of at least one programming language, such as Julia, Python, MATLAB, or R. During the course of study, the doctoral candidate will become familiar with selected methods drawn from dynamical systems theory, statistics, and information theory.

The dissertation will be carried out in cooperation with a partner external educational institution at the Institute of Measurement of the Slovak Academy of Sciences in Bratislava.

The aim of the dissertation is the development of a methodology for causal detection from measured time series, with a focus on stochastic dynamical systems.
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