Can I get a PhD in Stochastic Analysis given this limited background?

Given my limited background in stochastic analysis and other information (below), can I apply for a PhD with stochastic analysis for my dissertation topic?

1/4 I am currently a masteral student of mathematical finance, expecting to graduate sometime this year. I am taking up my second course Stochastic Calculus along with other subjects. I have already taken up one course in StoCal and one course in probability with measure theory.

Edit: Here are my other subjects in grad and undergrad that may be relevant:

(Duh: Calculus I, II, III, Linear Algebra, Elementary Probability), ODE, PDE, Statistics, Time Series, More Time Series, More Statistics (oh my!), Discrete Mathematics, Numerical Analysis, Real Analysis, NO Complex Analysis

2/4 One derivatives pricing course talked about martingales, measures, stochastic processes but those were taught heuristically there and rigorously in StoCal courses. So those 3 above are really my main background in Stochastic Analysis/Stochastic Calculus (whatever you call it).

3/4 I don't know about calculus of variations, Malliavin Calculus, different kinds of convergence of random variables, laws of large numbers, etc. We were not even given the full proof of Ito's lemma in classes.

4/4 My thesis is about credit risk, having mainly to do with statistics, the part of mathematical finance I don't want to go in to, if I were still interested in mathematical finance. Hence, I feel have no background in mathematical research given that the research conducted was mainly to do with statistics and finance.

Given my limited background in stochastic analysis and probability theory, can I already apply for a PhD in stochastic analysis?

If not, must I then take a master's in mathematics to see if I might take on stochastic analysis for another thesis? I just want to be really sure of my dissertation topic before I apply (as is expected of PhD applicants, right?).

So perhaps another thing to ask is: How do I know if I am ready to apply for a PhD with a certain dissertation topic in mind (in terms of the dissertation topic and not the readiness for the level of studies)?

Oh, more info:

1/2 I like to think I am very passionate about mathematics and am more interested studying stochastic calculus and probability more than my other classes. But never having done mathematical research, I don't know really if I am ready. I don't want to naively think what I have is enough.

2/2 I am not particularly interested in statistics, which is sort of related to probability. Hopefully, this isn't relevant...?