Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related representation formula, and asymptotics for the integral term in this formula.
"Moderate deviation probabilities for open convex sets: nonlogarithmic behavior." Ann. Probab. 32 (2) 1316 - 1355, April 2004. https://doi.org/10.1214/009117904000000216