PhD in Mathematics after Master's I'm currently pursuing my master's in statistics with probability specialisation. I am interested in stochastic calculus and want to apply for a PhD in math. My first year of master's includes a lot of stats courses. The second year is when I get to choose courses related to stochastic calculus.
The problem I have is I don't think I can do projects until the third semester. There are a couple of reasons for this:

There is no semester break and professors don't want to give a project during the semester
Most of the summer programmes are cancelled in my country.

I have excellent grades in my undergraduate and in master's so far. I have done two basic projects in my undergrad and one reading project under a professor in my master's. I have good letters of recommendations.
Do I have any chance of getting into math PhD programs in the US? What can I do to strengthen my application?
Courses I have taken in my undergrad: (grade - course contents)

Three analysis courses - got all As (real, multivariate, metric spaces)

Three Algebra courses - B in ring theory and A's in others (Linear algebra, group theory and ring theory)

Complex Analysis course - got an A

Topology (Till quotient topology in munkres) - got B

Complex Analysis - got an A

Differential Equations (existence, uniqueness, rectification etc.) - got an A

Calculus (Tensors and differential forms) - got an A

Two stochastic processes courses (Discrete and continous-time chains) - got A in both

Optimisation and game theory - A's in both


Courses taken in Master's: (marks are given instead of a grade)

Analysis - I ( scored  95/100), Probability (scored 90/100) + Bunch of statistics courses
Measure theoretic Probability, Analysis - II (taking them currently) + Bunch of statistics courses

Courses I plan to take:

Functional Analysis
Martingale theory
Ergodic theory
Brownian motion and diffusions
Markov Processes and Martingale Problems
Advanced functional analysis / PDEs
Theory of large deviations
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.