Prior to "opting for the herd" and leaving academia to work in the private sector, I began scribbling the details of what my PhD thesis might look like. The topic I was interested in writing my thesis on (at the time) was Lévy processes and in particular their applications to derivatives pricing. I began coding some of the more well-known price processes in R and added their descriptions along the way.
Since the following manuscript is merely a compilation of fragmented examples I intended to include in my PhD thesis, ignore any "lack of flow" that you may encounter.
I should also note that the mathematical representations of these Lévy processes exist in the risk-neutral domain, and require damping (or an alternative approach) to capture the risk premium of the Lévy process if one wishes to convert to the physical or real-world domain. The next update of the paper should discuss this in detail.