How will my studies in mathematical statistics be applied to and assist me with problems in chemistry?
Most definitely yes.

I took multiple statistics classes as an undergraduate and they have helped me considerably. (I can argue fairly that it helped me get tenure.)

A few suggestions from my own work:


Statistical design of multivariate experiments: Many scientists think you should test one variable at a time. No. I taught a grad student (in another group) about optimization theory and proper design and three months later, a great paper came out.
Data mining and exploration: Many chemistry data sets are extremely complicated, with cross-correlated factors. Understanding how to draw empirical inferences, find the most important factors, etc. is enormously helpful across a wide range of chemistry.
Principal component analysis: An emerging area in spectroscopy and imaging is taking complicated spectra and performing PCA to help with quantifying chemical components in mixtures and following everything from cancer growth to materials design. 
Multivariate regression and ANOVA: My group has created numerous quick statistical screens using multivariate surrogates for complex simulations or experiments.
Cross-validated analysis: Again, the understanding of training and test sets, bootstrapping, etc. is very useful.


Now, you also mention SDEs and Markov processes. These are crucial in chemical kinetics, including areas like reaction-diffusion systems. Monte Carlo methods are also highly used in studying dynamical processes.

The list would be enormous. Basically, I think it's a great skill to have and you'll use it throughout your career.