We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain Hölder-like norms of exponent greater than 1 /3. The proof uses a control of the variation of the Lévy area,under conditioning. The results are applied to the computation of the Onsager–Machlup functional of diffusion processes with constant diffusion matrix.
"Conditional Exponential Moments for Iterated Wiener Integrals." Ann. Probab. 27 (4) 1738 - 1749, October 1999. https://doi.org/10.1214/aop/1022874813