A Hitch-hiker's Guide to Stochastic Differential Equations: Solution Methods for Energetic Particle Transport in Space Physics and Astrophysics

摘要

In this review, an overview of the recent history of stochastic differentialequations (SDEs) in application to particle transport problems in space physicsand astrophysics is given. The aim is to present a helpful working guide to theliterature and at the same time introduce key principles of the SDE approachvia "toy models". Using these examples, we hope to provide an easy way fornewcomers to the field to use such methods in their own research. Aspectscovered are the solar modulation of cosmic rays, diffusive shock acceleration,galactic cosmic ray propagation and solar energetic particle transport. Webelieve that the SDE method, due to its simplicity and computational efficiencyon modern computer architectures, will be of significant relevance in energeticparticle studies in the years to come.