For anyone interested, here are a few links to academic articles I wrote during my PhD on probability theory.
I would say that one of the most pleasing parts of the work I completed for my thesis was that we managed to find the right mathematical way to describe a complex problem, which essentially made it much easier to express and solve problems which had previously used quite intensive techniques.
There articles show applications of the main ideas and contain lots of interesting work on martingales, measure changes, and some pretty ideas on filtrations too. Enjoy!
Fermat's Last Spreadsheet 