PhD in Mathematics after Master's
There isn't generally much of a barrier to making a small change of field after an MS. But there are two issues you may need to deal with. I suspect that for Stochastic Calculus a lot of background is needed in basic Analysis. Perhaps you have that already, but it might take some time (coursework) to get up to speed in that.
Projects/research in your background is good to have, but probably not the most important thing of all. Many people enter doctoral programs with little of that, though mostly from bachelors programs rather than masters.
The other time issue is that you need to pass comprehensive exams (qualifiers) in most math programs and they generally cover a fairly broad range (analysis, algebra, topology, ...) and you may need coursework to get ready for that.
But, changing to math from a field with similar research methods is not going to be a big issue, though you need a strong application generally as does everyone.