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

## TL;DR

This review introduces stochastic differential equations (SDEs) as effective tools for modeling energetic particle transport in space physics and astrophysics, emphasizing their simplicity and computational efficiency for recent and future research.

## Contribution

It provides a comprehensive overview of SDE methods applied to particle transport problems, including practical toy models for newcomers and a literature guide.

## Key findings

- SDE methods are effective for modeling cosmic ray modulation.
- They offer computational advantages for large-scale simulations.
- The approach is expected to be increasingly relevant in the field.

## Abstract

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via "toy models". Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.