Inferência de drift e difusão em sistemas estocásticos via dinâmica de Langevin

Abstract

In this paper we present a detailed development of the inference of terms of an equation of motion from real data, focusing especially on the modern theory of Brownian motion, which starts from the Langevin equation, which describes the stochastic dynamics of a system. Numerical simulation methods were applied in order to obtain a better prediction of the behavior of some dynamic systems, especially systems that use the Langevin equation to describe the movement of a particle subjected to a potential. We also studied differential equations as a whole. We obtained results for different simulated trajectories, which we were able to describe and infer the desired terms for each system quite satisfactorily. We were also able to observe a particle in three dimensions, bringing us closer to a detailed study of the real behavior of a complex system. The analysis of the data used to generate the simulations for each configuration in this work, as well as the development of the inference algorithm, were crucial to the progress of the research and the generation of the results.