In this thesis a data science study of elementary stochastic processes is laid, aided with the development of two numerical software programmes, applied to power-grid frequency studies and Dansgaard--Oeschger events in paleo-climate data.
Power-grid frequency is a key measure in power grid studies.
It comprises the balance of power in a power grid at any instance.
In this thesis an elementary Markovian Langevin-like stochastic process is employed, extending from existent literature, to show the basic elements of power-grid frequency dynamics can be modelled in such manner.
Through a data science study of power-grid frequency data, it is shown that fluctuations scale in an inverse square-root relation with their size, alike any other stochastic process, confirming previous theoretical results.
A simple Ornstein--Uhlenbeck is offered as a surrogate model for power-grid frequency dynamics, with a versatile input of driving deterministic functions, showing not surprisingly that driven stochastic processes with Gaussian noise do not necessarily show a Gaussian distribution.
A study of the correlations between recordings of power-grid frequency in the same power-grid system reveals they are correlated, but a theoretical understanding is yet to be developed.
A super-diffusive relaxation of amplitude synchronisation is shown to exist in space in coupled power-grid systems, whereas a linear relation is evidenced for the emergence of phase synchronisation.
Two Python software packages are designed, offering the possibility to extract conditional moments for Markovian stochastic processes of any dimension, with a particular application for Markovian jump-diffusion processes for one-dimensional timeseries.
Lastly, a study of Dansgaard--Oeschger events in recordings of paleoclimate data under the purview of bivariate Markovian jump-diffusion processes is proposed, augmented by a semi-theoretical study of bivariate stochastic processes, offering an explanation for the discontinuous transitions in these events and showing the existence of deterministic couplings between the recordings of the dust concentration and a proxy for the atmospheric temperature
