Statistical Inference and Model Discrimination in Stochastic Dynamical Systems

Minimal stochastic models have provided essential insights into the dynamics of complex systems in fields such as ecology, epidemiology, economics, and climate science. However, systematic methods for estimating model parameters from data, as well as rigorous approaches to determine which model best describes a given dataset, remain limited and continue to generate scientific debate. This thesis project will focus on parametric inference in the setting of stochastic differential equations, with particular attention to maximum likelihood estimators formulated at the level of stochastic paths. The work will extend existing inference frameworks to jumping processes, which would enable a systematic distinction between continuous and discrete state models. The project has the potential to offer new empirical insights into the design of more efficient experimental protocols that could reduce errors in parametric estimations and enhance model distinguishability. Furthermore, this framework can be applied to real-world datasets, thereby linking theoretical innovation with practical relevance.