We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the proof of the upper bound is more complicated.
"Moderate deviations for recursive stochastic algorithms." Stoch. Syst. 5 (1) 87 - 119, 2015. https://doi.org/10.1214/14-SSY138