# Large Deviations Rate of Convergence and Robbins Monro

I am looking for a result/paper (if there is any) on the large deviations rate of convergence of the Robbins-Monro (RM) algorithm. Specifically, given $$X_k \rightarrow X$$ a.s. in the RM algorithm, I would like a result of the form $$\lim_{k \rightarrow \infty} \frac{1}{k} | X_k - X | = c$$. Thanks!