There seems to be way more 3rd party plugins. Reaper has quite an extensive API while Ardour is open source. There was quite a long discussion about this on the Ardour forum. It seems that the Reaper API and general extensibility gained more traction than Ardour being open source, as counter intuitive as that seems. Having used both pieces of software a reasonable amount, Reaper has a slight edge in terms of usability and customisation of the layout and look and feel. In particular the midi editing is smoother. That said, Ardour is a fantastic piece of software and a great open source success.
LV2 plugins aren't supported in Reaper but are in Ardour, this makes quite a difference in Linux. In my opinion the anywhere to anywhere routing is better in Ardour. That said, I moved from Ardour to Reaper and prefer Reaper.
I've tried using it but it crashes too often and is generally too buggy to use. It seems to be in an early stage of development so this is to be expected. The UI and general workflow look very promising though, in particular the piano roll. It has a long way to go to match the maturity and features of Ardour, but the UI design that it's aiming for will make it more suitable for people making EDM.
There are other models that take into account jumps in the prices/market. As for retail traders using these models, I think it is not recommended and not practical.
Are you looking for a proof of Girsanov's theorem or an explanation of how it is used to price? A good reference is Oksendal [0], but it's still quite tough going. As for how it's used, a good reference is Shreve's second volume [1], which also contains a proof of Girsanov's theorem. Joshi's book [2] is a little bit lighter on the mathematical rigour.
A quick explanation of how it's used:
Taking the stochastic differential equation for geometric Brownian motion, apply Girsanov's theorem to change measure via a drift change such that we now have a discounted stock price that is a martingale. The discounted stock price is the stock price divided by a short term bond or cash account asset. In this new measure the discounted short term bond/cash account asset is also trivially a martingale since it's being divided by itself. So we have that our two key assets (discounted) are martingales. We then define the time zero price of the option (divided by the time zero price of the bond/cash asset) to be the discounted expected value of its value at maturity in this newly constructed measure. By construction this discounted option price is a martingale and we now have three assets that are all martingales which implies there is no arbitrage possible. With this option price, called the "risk neutral" price, no arbitrage is possible under our newly constructed measure, but, because the original measure is an equivalent measure no arbitrage is possible here in the "real world" either and so this is our actual price.
I appreciate there are a few steps here that seem like a bit of a leap. It took me a while to appreciate them. The key things to appreciate are:
How everything being a martingale implies a lack of arbitrage. Girsanov allows you to make your (discounted) underlying a martingale.
How you can then just make the option price a martingale by construction. And then how lack of arbitrage under one measure means lack of arbitrage in any equivalent measure.
The discounting can also be a little confusing, but it's really just incorporating the time value of money into the calculations.
[0] Oksendal B . Stochastic Differential Equations.
[1] Shreve S E. Stochastic Calculus for Finance II.
[2] Joshi M S. The Concepts and Practice of Mathematical Finance