Stochastic differential equations (SDEs) can be used to describe cosmic ray transport in an efficient way suited for modelling on modern computing architectures. In this talk I will give an overview on how to transform Fokker-Planck (partial differential) equations into their corresponding set of SDEs and show how to solve them numerically.
Based on the open source simulation framework CRPropa we have developed a flexible SDE solver in the past years. I will demonstrate the versatility of the framework with application on focused pitch angle diffusion and transport in time-evolving wind bubbles. The first one is relevant in heliospheric transport of solar energetic particles. The latter one is connected to the search for Galactic PeVatrons, sources of Galactic cosmic rays reaching super-PeV energies.