I understand that it's possible, thankfully, to have your dissertation in a different topic from your master's thesis, but I seem to have a problem (see below). Do you know any other problems might I run into?
Background on me:
I am finishing up my master's in mathematical finance and now plan to pursue a PhD with my dissertation being in stochastic analysis/calculus, a branch of mathematics used in finance and physics.
My background on stochastic analysis:
I have had 3 classes related to stochastic analysis and 2 classes applying the concepts.
The ONLY time stochastic analysis ever came up was encountering something in a paper that gives probabilities in the Q-side, and I thought of using a theorem to convert them to the P-side but later found out the paper was unnecessary or inapplicable (I forgot; I think I figured out another solution).
One problem I seem to have:
Some PhD applications seem to require a PhD proposal including a hypothesis, literature review and methodology.
I am not quite sure how mathematical research is conducted. Most of my research has been mainly in finance and statistics. What might I be able to do about this?
I am considering taking a second master's if needed but hopefully it need not come to that.