Currently finishing up my bachelor's thesis. The content can roughly be described as extreme value theory of stochastic processes.

The main part of the thesis is based on a very recent paper (july 2022). It basically extended known results for time series (stochastic processes in discrete time) to continuous-time stochastic processes. Therefore i'm explaining the results given in this new paper and perhaps compare them with previous results about time series.

Additionally, and this will almost always be necessary for a bachelor's thesis, you'll need to give some brief introduction to relevant prerequisite marerial. In my case this means writing a bit about multivariate extreme value theory and about (càdlàg) stochastic processes, their topology (J1 topology) and weak convergence.

Then as some 'bonus', i develope some original results (though not too novel results imo) for special cases of stochastic processes, specifically Markov processes. For a bachelor's thesis you aren't really expected to develope original results, but it's certainly possible to some degree and it'll likely lead to a better grade.

As to how i found the topic i wanted to write about: I just looked at a journal my professor was an editor of and searched for something that seemed interesting. Then contacted that professor to ask whether it would be possible to write my thesis about this paper and it was quickly approved.